5

The firit 50 five dirit nmherz form the Rand] = Millinn Randlom Digits with IO(HIO Normal Deviates book (shown Ahut Feceled [0,1] (by dividing by LUUQU) end then ...

Question

The firit 50 five dirit nmherz form the Rand] = Millinn Randlom Digits with IO(HIO Normal Deviates book (shown Ahut Feceled [0,1] (by dividing by LUUQU) end then all numbers 0.6 are Tetained. We can consier 3 Terained numbers As rAMdomSH Irul Weg U(0. 0.6) distribution.10097 39292 10402 02560 09376 3614732533 37542 00922 15953 38311 3655313586 04805 08422 34764 31165 1687734673 24805 19645 35080 04435 1217154876 '24037 09303 33606 2765909117 20536 23209 02529 12807Pretend the threshold 0.

The firit 50 five dirit nmherz form the Rand] = Millinn Randlom Digits with IO(HIO Normal Deviates book (shown Ahut Feceled [0,1] (by dividing by LUUQU) end then all numbers 0.6 are Tetained. We can consier 3 Terained numbers As rAMdomSH Irul Weg U(0. 0.6) distribution. 10097 39292 10402 02560 09376 36147 32533 37542 00922 15953 38311 36553 13586 04805 08422 34764 31165 16877 34673 24805 19645 35080 04435 12171 54876 '24037 09303 33606 27659 09117 20536 23209 02529 12807 Pretend the threshold 0.6 nOL kuown that 1 Ramne ITon unorn U(u distribution, w7th be extimated, Let M be the MAXIMUIL the Tetained Ralbl The likeliliood tul that 0.j 4076. (u . II 1(0 > u) 0-% 1(0 > MA where 1(A) is [ if [Tue 13 fa/se, ARSm- tolinformative ( Jellieys prior 7(01 1(0 > 0. Fosterior depends dnta via the maximum M and belongs Pule,a) wich denlity the Fareto family. 67 1(0 > c) What are and c? Estinall 4d cakculale 95% cquitailer credibk *. Value HaTAlele (0.6) in the cedible set? Mit: Expectation of the Pareto Pa(c,a) is and CDF 1s F(0) = (1 - (c/oj"] 1(0 > c). It



Answers

The joint cumulative distribution function of two random variables $X$ and $Y,$ denoted by
$F(x, y),$ is defined by
$F(x, y)=P[(X \leq x) \cap(Y \leq y)] \quad-\infty<x<\infty, \quad-\infty<y<\infty$
(a) Suppose that $X$ and $Y$ are both continuous variables. Once the joint cdf is available, explain
how it can be used to determine $P((X, Y) \in A),$ where $A$ is the rectangular region $\{(x, y)$ :
$\quad a \leq x \leq b, c \leq y \leq d \}$
(b) Suppose the only possible values of $X$ and $Y$ are $0,1,2, \ldots$ and consider the values $a=5$$b=10, c=2,$ and $d=6$ for the rectangle specified in (a). Describe how you would use
the joint cdf to calculate the probability that the pair $(X, Y)$ falls in the rectangle. More$d$ are all integers?
(c) Determine the joint cdf for the scenario of Example 4.1. [Hint: First determine $F(x, y)$ for$x=100,250$ and $y=0,100,$ and $200 .$ Then describe the joint cdf for various other $(x, y)$
pairs. $]$
(d) Determine the joint cdf for the scenario of Example 4.3 and use it to calculate theprobability that $X$ and $Y$ are both between. 25 and. $75 .$ [Hint: For $0 \leq x \leq 1$ and $0 \leq y$ $\leq 1, F(x, y)=\int_{0}^{x} \int_{0}^{y} f(u, v) d v d u . ]$
(e) Determine the joint cdf for the scenario of Example $4.4 .[$Hint: Proceed as in $(\mathrm{d}),$ but be careful about the order of integration and consider separately $(x, y)$ points that lie inside the triangular region of positive density and then points that lie outside this region.

Hi here according to the question is given that X one X two X three export X five follows caution distribution with the median theater And Scale Parameter one. Now the pdf of this distribution exceed acquires too one by buy into one whole liver it by one plus x minus the square minus in 20 less than x. Less than theater minus in pretty less than -3 Treaty less than X less than infinity. Sorry I missed ready earlier managing fridge in less than three to less than X mosquito otherwise. So first we have to show that Emily of theater tested ahead can be far can be found by minimizing minimizing the function submission items from 12 and no one plus X. I minus theater square secondly in our function has been given all the scripts has been given we have to approximate the amelia of theater by plotting dysfunction. Okay. No start with our problems. See to find the family of theta we constructed like loot function which is given by L theater explain is equal is to Product of items from one point effort exciting colon theater. He's close to one by buy into the boring one. Holy wedded by product of items from one to win one plus it's I minus theta square. Yeah, no maximising the likelihood function is evil into maximizing the log likelihood function. Now take the log likelihood function because this maximizing this likelihood function is equivalent to maximizing log likelihood function because law is increasing function of X Equals two script. Tell theatre explained question minus in love by my nurse Submission Islands from 1 to win lava one plus X. I minus theta square. Okay. See Emily of Tiger is such a value bad. It maximizes the log likelihood function. No log likelihood function. That is a script. L Thanks girl is maximum. That implies Submission items from one. Doing log one plus except my nasty to square. This function is minimum because there is a negative seen before this function. So scriptural Theodoric skeletons maximum when this dysfunction at its minimum. So clearly we can say that the Emily of theater theater head can be found by minimizing minimizing the function submission items from one doing log one plus exit I minus theta square. Okay so we have already proved our first problem. I'm going forward to the second problem. She in our will plot the graph of this function and approximate the value of Emily. So for this problem, realization of 500 variables are given X one equals two minus one point 94 X two equals 2 0.59 Eggs three words to -5.98 eggs four Equals 2 -0.08 X five question when a zero 77. Now I have done in our using the scripts which has been given in the question and taking the scripture from it. I'll show you see I have taken the values of the real additions our values of eggs in a vector X. Within a contract mission function. Okay then I have taken three to according your questions to is minus 6 to 6. And gap is 01001. So everything I have written according to the question and then when I executed the craft I got the graph like this. Okay now it is very evident that this function, the function, summation, log one plus X a minus theater square. See the function it is elephants given elephants. Is this function? Okay now the graph, this is the values of this function. The craft were blocked from here. Now the this graph Adams minimum values somewhere this Okay now we have to see that for which value of theta it against the minimum value. Okay now We do one thing with plotted line to see what is the minimum value of he died. Okay see from here it is evident that somewhere when Theta equals 2 -2 0153. Yeah the fellow of this function is maximum. So now the value of Some mentioned irons from 1 to N log one plus examiners. Theatre Square Yes, minimum when theta equals two minus 0.53. So clearly from the graph we get that the family of tita tita had Emily did, I had Emily equals 2 0 53. This is the answer. Thank you

I This again is one experiment that you have to kill out. Specially interesting experiment, uh, which we drive from Mom under Carlos Metal finding ability. And, um, in this case, you are going to use a simple definition of probability which says the probability off in event is it close to the number of successful outcomes off the studio Sambo space. So that's what German Jews. And you can use your calculator your t i a n four plus, and then you you sent it to the correct amount. And in this guess you want to be waking on. Ah, two days that are being award and we are going to repeat the experiment 50 times. Uh then after 50 times, you have to go to their doubts. And, um, when there's out that you have noted, the first part of the person is that you're supposed to find the probability that this some is nine or more. So you just count how many name or a number which is greater than nine is a sound? What do you find? And in the second case, you also supposed to find the probability that the sum is less than these are in session. So which is you? Some off true Islam or three Summer four is on the show. Life's on six, okay, and seven is not included there. But in the offense tickets where you wanted to some off 99 is included. Or more so the sum is always up to talk toward his eyes, so it will be 9 10 11 and 12 that you'll be checking off. You come all the substance Slocum's. Then you divide by by 50 petitions that you give that and you actually see that there is also always fluctuating for the first person. They will be fluctuating on, uh, between 5 18 and in the second case around faithful 12.

I This again is one experiment that you have to kill out. Specially interesting experiment, uh, which we drive from Mom under Carlos Metal finding ability. And, um, in this case, you are going to use a simple definition of probability which says the probability off in event is it close to the number of successful outcomes off the studio Sambo space. So that's what German Jews. And you can use your calculator your t i a n four plus, and then you you sent it to the correct amount. And in this guess you want to be waking on. Ah, two days that are being award and we are going to repeat the experiment 50 times. Uh then after 50 times, you have to go to their doubts. And, um, when there's out that you have noted, the first part of the person is that you're supposed to find the probability that this some is nine or more. So you just count how many name or a number which is greater than nine is a sound? What do you find? And in the second case, you also supposed to find the probability that the sum is less than these are in session. So which is you? Some off true Islam or three Summer four is on the show. Life's on six, okay, and seven is not included there. But in the offense tickets where you wanted to some off 99 is included. Or more so the sum is always up to talk toward his eyes, so it will be 9 10 11 and 12 that you'll be checking off. You come all the substance Slocum's. Then you divide by by 50 petitions that you give that and you actually see that there is also always fluctuating for the first person. They will be fluctuating on, uh, between 5 18 and in the second case around faithful 12.

We're going to simulate the half normal distribution whose pdf is shown here using the accept reject method with the candidate distribution G of X is equal to eat The minus X for part A were asked to find the inverse CDF corresponding to G of X, which will allow us to simulate values from this distribution. This is simply the exponential distribution with Lambda set to one. So we know that at CDF is given by the following. And now to find the inverse CDF, we can set you equal to GRX and then solve for X. And we have negative log of one minus you. So that is the inverse CDF of GDX Next for part B were asked to find the smallest major ization constant that is, we want to find the smallest constant such that it is always at least a zbig as f X over GDX. So if we find FX over GDX, we get the following. So now we want to find the maximum value that this could possibly be and set that exactly equal to see or rather set see exactly to that this maximum occurs when this is maximized and weaken. Find except corresponds to the maximum of that by setting the first derivative of this value equal to zero, and we end up with X is equal to one. So if we plug one into the equation, we have C is equal to the square root of two over pie 10 z to the exponents. One half that's about 1.3155 Then for part C, we're asked for the expected number of candidate values that would be required to generate 10,000 accepted values. So this is given by end time, see and as the number of accepted values that are desired. So that's 10,000 time see, and it gives us 13,000 155. So on average, we would need to generate 13,155 candidate values to end up with 10,000 accepted values. And finally, for part D were s to write a program to simulate 10,000 values from the half normal distribution. Now the acceptance criterion is given by the random uniformed variable that has drawn time see times are candidate distribution being at most equal to the density at why and just rearranging this we have you is listener equal to you? Is that why? Divided by G. L Y divided by a C that we already have f over g right here and we have C so this could be simplified to the following. So the steps for the program are one. We draw a random variable from our candidate distribution. So we call that why to we draw from the the uniform distribution, the standard uniform distribution and then three we test our criterion. So if our criterion is met, then we accept the generated value and then we repeat these three steps until we have 10,000 variants and then we will have 10,000 vary. It's from the half normal distribution. So the R code that I produced looks like this. So in step one, we draw from our candidate distribution using the inverse CDF method. In step two, we draw from the uniform standard uniform distribution and Step three. We test our acceptance criterion. If it's accepted, then value gets placed in the Vector X, and it gets repeated until we have a vector X of size 10,000


Similar Solved Questions

5 answers
2. Find the general solution to the following homogeneous differential equation: y"+4y' -y =0
2. Find the general solution to the following homogeneous differential equation: y"+4y' -y =0...
5 answers
Page 0f 18Questionpoint)Find the length of the graph of f(c) 1)3/2 , ,1 < € <4. Round your answer to three decimal places:Page of 18
Page 0f 18 Question point) Find the length of the graph of f(c) 1)3/2 , ,1 < € <4. Round your answer to three decimal places: Page of 18...
5 answers
An car iitially at test cxpcrences accekration of ] 40 I ofithe objccth acia"c !clocuy orer thc J4 Intcrlthcn tratckUclocin for aothcr 40 , What Enc mhentuda
An car iitially at test cxpcrences accekration of ] 40 I ofithe objccth acia"c !clocuy orer thc J4 Intcrl thcn tratck Uclocin for aothcr 40 , What Enc mhentuda...
5 answers
Yuestion 10 (2 pointsi A narrow beam of light enters block of glass as shown: Which arrow best represents the path of the light in the glass block?
Yuestion 10 (2 pointsi A narrow beam of light enters block of glass as shown: Which arrow best represents the path of the light in the glass block?...
5 answers
ConsimnArlene walk act055 "high wiro stung cntonia bolween two buildings 15. LaDan The sag the rope whon sho at Ihe midpolnt = ghown figure (FigurePanaKcermassnaime tuntnta rOpc at this pont?Figurao AEd1452SubmltPrayeouutananturt HequeuluaneuefIYIncorrect; Try Agaln;- eltampta ruqalnlng
Consimn Arlene walk act055 "high wiro stung cntonia bolween two buildings 15. LaDan The sag the rope whon sho at Ihe midpolnt = ghown figure (Figure Pana Kcermass nai me tuntn ta rOpc at this pont? Figura o AEd 1452 Submlt Prayeouutananturt Hequeuluaneuef IY Incorrect; Try Agaln;- eltampta ruqa...
5 answers
Gudeter 3, Sectlon 3.6, Quastlon 10Thei nonhomogeneous equation /' Y" _ 2y = 23 /2 _ 1,/ > 0,has homogeneous solutions Y1 1(5rYE Particular solution to the nonhomogeneous equation that does nOt involve any terms from the E ()m tEla & homogencous solution.Enter an exact answerEnclose arguments of functions parentheses. For example, sin (2x)Y(Cllck # you would Ilke to Show Work for thie question: Qpen Show Work
Gudeter 3, Sectlon 3.6, Quastlon 10 Thei nonhomogeneous equation /' Y" _ 2y = 23 /2 _ 1,/ > 0,has homogeneous solutions Y1 1(5rYE Particular solution to the nonhomogeneous equation that does nOt involve any terms from the E ()m tEla & homogencous solution. Enter an exact answer Encl...
5 answers
"Note: For all the questions, provide detalled solution steps:Question 1:(50 points)Find the derivative of the function (and simplify the results);(a) f(x) = (e' +X)(30 points)(b) 9 (x) = x2cos *(20 points)Question Z(50 points)Find the derivative of the function (and simplify the result):64 f(x)
"Note: For all the questions, provide detalled solution steps: Question 1: (50 points) Find the derivative of the function (and simplify the results); (a) f(x) = (e' +X) (30 points) (b) 9 (x) = x2 cos * (20 points) Question Z (50 points) Find the derivative of the function (and simplify th...
5 answers
Pant: : / 2Par 2 cf 3BePar: ? / ]Parr 3 0l 3
Pant: : / 2 Par 2 cf 3 Be Par: ? / ] Parr 3 0l 3...
5 answers
Name the structure at the blue arrow in the electron micrograph shown below:nucleusrough endoplasmic reticulumGolgi apparatussmooth endoplasmic reticulum
Name the structure at the blue arrow in the electron micrograph shown below: nucleus rough endoplasmic reticulum Golgi apparatus smooth endoplasmic reticulum...
5 answers
A=7 ? Is the given function continuous at x2_49 if*#7 f(x) = X-7 if*=7Solution:f(a)lim f (x) X-alimf (x)f(a)f(x) isat a =7_
a=7 ? Is the given function continuous at x2_49 if*#7 f(x) = X-7 if*=7 Solution: f(a) lim f (x) X-a limf (x) f(a) f(x) is at a =7_...
1 answers
Knowing that at the instant shown bar $A B$ has an angular velocity of 4 rad/s and an angular acceleration of $2 \mathrm{rad} / \mathrm{s}^{2}$ both clockwise, determine the angular acceleration $(a)$ of bar $B D$ (b) of bar $D E$ by using the vector approach as is done in Sample Prob. 15.8
Knowing that at the instant shown bar $A B$ has an angular velocity of 4 rad/s and an angular acceleration of $2 \mathrm{rad} / \mathrm{s}^{2}$ both clockwise, determine the angular acceleration $(a)$ of bar $B D$ (b) of bar $D E$ by using the vector approach as is done in Sample Prob. 15.8...
5 answers
The figure shows a system with two polarizers that can be rotated, with the angles being measure from the vertical direction: The angle of the first polarizer is 0,-309.What should be the angle 8, of the second polarizerif the incident beam in the figure is unpolarized with an intensity of 12 Wm?, and you want the exiting beam to have an intensity of 2.0 W/m??
The figure shows a system with two polarizers that can be rotated, with the angles being measure from the vertical direction: The angle of the first polarizer is 0,-309.What should be the angle 8, of the second polarizerif the incident beam in the figure is unpolarized with an intensity of 12 Wm?, a...
5 answers
Which option describes the polarity of the ED2G molecule shown below?120.00AtomElectronegativity 3.442.82.2NonpolarPolar with a molecular dipole pointing upPolar with a molecular dipole point down
Which option describes the polarity of the ED2G molecule shown below? 120.00 Atom Electronegativity 3.44 2.8 2.2 Nonpolar Polar with a molecular dipole pointing up Polar with a molecular dipole point down...
5 answers
9. The function Alt) = 300e 0014 gives the amount of aspirin in milligrams in & patient 's bloodstream minutes afiter the aspirin has been administered Find the initial amount of aspirin administeredb) Find the amount of aspirin in the patient '= bloodstream after 20 minutes_How long does it take for the amount of aspirin to be half the initial amount administered?
9. The function Alt) = 300e 0014 gives the amount of aspirin in milligrams in & patient 's bloodstream minutes afiter the aspirin has been administered Find the initial amount of aspirin administered b) Find the amount of aspirin in the patient '= bloodstream after 20 minutes_ How lon...
5 answers
A 5.0-kg block is pushed 3.0 m up a smooth (friction-less)vertical wall with constant speed by a constant force of magnitudeF applied at an angle of θ = 60° above the horizontal. Determinethe normal force that the wall exerts on the block.
A 5.0-kg block is pushed 3.0 m up a smooth (friction-less) vertical wall with constant speed by a constant force of magnitude F applied at an angle of θ = 60° above the horizontal. Determine the normal force that the wall exerts on the block....
5 answers
Balance the following equation and enter your answers in thie appropriate boxes Note; If the answer is you must enter in the blank to receive full credit: The size of the boxes are large and could not adjust t0 Smaller sizc;NaBrCaFzNaFCaBrzNaBrCF NAF1HRNM
Balance the following equation and enter your answers in thie appropriate boxes Note; If the answer is you must enter in the blank to receive full credit: The size of the boxes are large and could not adjust t0 Smaller sizc; NaBr CaFz NaF CaBrz NaBr CF NAF 1 H R N M...
5 answers
Which statement is incorrect regarding Type IV Hypersensitivity: A) Type hypersensitivity is a cell mediated response: Ivy is - an example of Type IV hypersensitivity B) Poison with skin protein to form an antigen Small chemical substance interacts and skin protein results in a limited D) Initial contact with the small chemical response and likely no dermatitis the altered skin cells, leading to itchy E) T-helper cells are activated to destroy red bumps
Which statement is incorrect regarding Type IV Hypersensitivity: A) Type hypersensitivity is a cell mediated response: Ivy is - an example of Type IV hypersensitivity B) Poison with skin protein to form an antigen Small chemical substance interacts and skin protein results in a limited D) Initial c...

-- 0.020141--