5

Not yet answered Points Out 0f 15 F Flag questionSuppose X is a uniform random variable with the following properties P(X < 8.7) = P(X > 8.7) and2P(X < 3.1...

Question

Not yet answered Points Out 0f 15 F Flag questionSuppose X is a uniform random variable with the following properties P(X < 8.7) = P(X > 8.7) and2P(X < 3.1) = P(X231).What is the probability P(X < 5.9)?0.255 b. 0.333 0.417 d. 0.00 0.500

Not yet answered Points Out 0f 15 F Flag question Suppose X is a uniform random variable with the following properties P(X < 8.7) = P(X > 8.7) and 2P(X < 3.1) = P(X231). What is the probability P(X < 5.9)? 0.255 b. 0.333 0.417 d. 0.00 0.500



Answers

The random variable $X$ has the following probability distribution: $$ \begin{array}{lllll} x & 2 & 3 & 5 & 8 \\ \text { Probability } & 0.2 & 0.4 & 0.3 & 0.1 \end{array} $$ Determine the following: (a) $P(X \leq 3)$ (b) $P(X > 2.5)$ (c) $P(2.7 < X < 5.1)$ (d) $E(\mathrm{X})$ (e) $V(\mathrm{X})$

In this problem, the probability distribution of the random variable X is given. We have to determine the probabilities asked. The first probability asked is probability of X Less than or equal to three. In the given table. We can see that X less than or equal to three means either X is equal to two, or X is equal to three. So the probability of X less than or equal to three is equal to Probability of x equal to two plus Probability of x equal to three. This is equal to Probability of x equal to two is 0.2 plus Probability of x equal to three is 0.4. This is equal to 0.6. So probability of x less than the required two, 0.6. Next it is asked to find the probability of X greater than 2.5. In the given table we can see that X greater than 2.5 means X is either 35 or eight. So probability of x greater than 2.5 is probability of X equal to three Plus probability of x equal to five Plus probability of x equal to eight. This is equal to Probability of x equal to three. probability of x equal to five. And probability of x equal to eight. So this is equal to 0.4 Plus 0.3 Plus 0.1. This is equal to 0.8. So the probability of x greater than 2.5 is 0.8. Next disaster probably tee off X line between 2.7 And 5.1. That is the probability of 2.7 less than X. less than 5.1. In the given table. We can see that between 2.7 and 5.1 we have the values three and five. So this is equal to probability of X equal to three plus. Probably Dios X equal to five, Probability of x equal to three is 0.4 and probability of x equal to five is 0.3, so this is equal to 0.4 Plus 0.3. This is equal to 0.7. So the probability of x line between 2.7 and 5.1 is 0.7 next disaster expected of X. That is expected X. We have to find expected X. This is equal to submission of X into probability of X equal to X overall X. So this is equal to two Into 0.2, probability of X equal to two is 0.2, so two in 20.2 plus three in 2, probability of x equal to three is 0.4. So three in 20.4 Plus five in 2, probability of X equal to 50.3, So five in 20.3 plus eight in 2, probability of X equal to 80.1. So eight in 20.1, this is equal to 0.4, There's 1.2 Plus 1.5 Plus 0.8. The sum is equal to 3.9. So expected X is equal to 3.9. Next disaster variance of eggs, we know that variance of X is equal to submission over all eggs, X square into probability of X equal to x minus mean square, that is minus square off expected eggs. This is our variance of X. So this is equal to To square, that is four in 2, probability of X equal to two is 0.2, so four in 20.2 plus three square. That is nine and 20.4 Plus five square that is 25 In two, 0.3 Plus eight square that is 64 In two, 0.1 Probability of x equal to eight, so 64 into 0.1 minus expected X square. The test 3.9 sq this is equal to 0.8 Plus 3.6 Plus 7.5 Plus 6.4 -15.21. And finally, this is equal to three point 09. So variance of X is equal to 3.09

For a continuous random variable. We are given the probability density function F of x equals x over eight. For X is between three and five. And were asked to solve for several probabilities For anywhere. S defying the probability that X is less than four. This will be the integral From 3 to 4. Yeah. Of our density function, which will be X squared Over 16, evaluated from 3 to 4, Which is equal to 1 -9/16. 4.4, for part B. Were asked to sell the probability that X Is greater than 3.5. So we integrate from 3.5 up to the maximum range of X, which is five of the density function. And this comes out to a probability of about .7969 for part C we've solved the probability that X is between four and 5. That's 25/16 -16/16, Which is 9/16. Yeah, Or approximately .56- five. Be asked for the probability that X is less than 4.5. This probability comes out 2.7031. And for e were asked for the probability that x is less than 3.5, or X is greater than 4.5. Since these Eriks exclusively mutually exclusive outcomes and it's an or operator, This is equal to the sum of these two probabilities. Now this is equal to the integral From 3 to 3.5 of our density function. Mhm plus the integral from 4.5 to 5, And this comes out to the probability of .5.

In this problem we will find first E is the probably hoping that number is praying. The prime numbers are 2 3, 5 and seven. The probabilities some of those probabilities .223 At this .20. Yes 0.7 Similarly, P F is the probability that the number is less than four, so it can be 12 or three probability yes 0.1 size Less .23. This point 12 now probably be E intersection F. That is it is prime, and less than four is probability of getting two or three, which is .23 plus .12. You know that the union F has nothing, but E must be F minus B. The intersection of substituting the values we get .6 to this point one kind, which is equals two 0.77

So 75. A random number generator picks a number from 1 to 9 in a uniform. So a just wants the notation. We know it's uniforms. Smallest numbers. One largest number is nine. Be the graph of the probability distribution goes from one 29 The height is one over B minus A. So one over nine minus one gives me a knew me. Just make a rectangle. See the f of X. We have two options. 1/8 or zero. The probability is 1/8 anywhere from one 29 everywhere else is zero D is the me a plus B over too one plus nine over, too. That's 10 over, too. That is five e the standard deviation. It is the square root of me, minus a squared over 12 to the square root of eight squared over 12 and that is approximately 2.309 if the probability that X is between 3.5 and 7.25 so it's really just the area of a rectangle. Zo. The base is 7.25 minus 3.5 times the height, which is 1/8 and that is 0.469 g. The Probability X is greater than 5.67 So once again similar to F is from nine toe 5.67 That's the base times the height that is 0.416 h. The probability P is greater than five. Given X is greater than three. So the probability that both those are true is the probability that X is greater than five. The denominator is always the gin in part, so the probability that X is greater than 30. So the probability that X is greater than five is nine minus five times 1/8 and the denominator nine minus three times 1/8 one. These cancel so four over six, which is 0.667 and I find the 90th percentile. So we know the area 0.9 the area of a rectangle, so we'd be the bottom 90%. So from some K minus one times the height, which is 1/8 kind, both sides by eight 7.2 equals came on. This one had won the both sides and K equals 8.2 off


Similar Solved Questions

5 answers
Lt J(r,V) pts) Find 1(3 pts) Finual 1pL ) 11{
Lt J(r,V) pts) Find 1 (3 pts) Finual 1 pL ) 1 1 {...
5 answers
Steps to balancing: 1- Determine the valence of all element's 2- Determine the number of e- trans as written 3- Balance e - 4- Balance non-redox elements (not H/O) 5- Balance oxygen w H2O, and Balance H2O with H+ 6- Check charge Balance
Steps to balancing: 1- Determine the valence of all element's 2- Determine the number of e- trans as written 3- Balance e - 4- Balance non-redox elements (not H/O) 5- Balance oxygen w H2O, and Balance H2O with H+ 6- Check charge Balance...
5 answers
Assume that the complete combustion one mole of glucose carbon (AG" dioxide and water libcrates 2870 kJlmol 2870 kJlmol) If one contraction cycle in muscle requires 67 kI , and the energy from the combustion of glucose efliciency of 39% t0 contraction; how many contraction cycles could converted with an thevretically [ueled by the complete combustion of one mole of glucose? Round your answer to the nearest whole number:cyeles per mole glucose
Assume that the complete combustion one mole of glucose carbon (AG" dioxide and water libcrates 2870 kJlmol 2870 kJlmol) If one contraction cycle in muscle requires 67 kI , and the energy from the combustion of glucose efliciency of 39% t0 contraction; how many contraction cycles could convert...
5 answers
Use the product Rule to find the derivative Of the function f (x)=x('+3)Find the derivative Of the function f (x)= +6x6. Find the derivative of the function f (x)= 3X-20 T+4 State which diflerentiation rule(s) you used t0 find the derivative
Use the product Rule to find the derivative Of the function f (x)=x('+3) Find the derivative Of the function f (x)= +6x 6. Find the derivative of the function f (x)= 3X-20 T+4 State which diflerentiation rule(s) you used t0 find the derivative...
5 answers
5:12 <EXPERIMENT # 4: Attempt`Question-/10pH; MEASUREMENT AND APPLICATIONA: Determination of pH Through the use of Indicators:Estimate the pH of each solution; based on the observed color change when an indicator added to the solution:0.10 Msolutions HCI NaHZPO4HC2H3O2ZnS04Methyl Violetblue violetvioletviolcomipleledSave for LaterSubmit
5:12 < EXPERIMENT # 4: Attempt` Question -/10 pH; MEASUREMENT AND APPLICATION A: Determination of pH Through the use of Indicators: Estimate the pH of each solution; based on the observed color change when an indicator added to the solution: 0.10 Msolutions HCI NaHZPO4 HC2H3O2 ZnS04 Methyl Violet...
5 answers
1 2 H 0 8 1 5 % 1 1 + # 8 Tlu Tlo Sl" 2 2 0 6 6 08 89
1 2 H 0 8 1 5 % 1 1 + # 8 Tlu Tlo Sl" 2 2 0 6 6 0 8 8 9...
5 answers
Para Kkriqt 7,071Graph te follawing Parabolapalrakek Irint 4,0]9the distance Octwccn (7 3) and (2, 2)(Enter Your answtr =comma-ccoarated Ist)
para Kkriqt 7,071 Graph te follawing Parabola palrakek Irint 4,0]9 the distance Octwccn (7 3) and (2, 2) (Enter Your answtr = comma-ccoarated Ist)...
5 answers
3478sgrt(3).y + 42y1380
347 8sgrt(3).y + 42y 1380...
5 answers
U-2 +4 +C 3ax_3sinx+3Sin p81 U_Sec? (ax) Sin (ax) dx
U-2 +4 +C 3ax_3sinx+3Sin p8 1 U_Sec? (ax) Sin (ax) dx...
1 answers
Consider the following four jobs singl machine for T-problem. Continue B&B procedures until you have the first trial solution and once YOu encounter the first trial solution, show your process to fathom unnecessary nodes (simply cross-out all nodes that can be eliminated).JobP(u)P(4)P(I)P(2)
Consider the following four jobs singl machine for T-problem. Continue B&B procedures until you have the first trial solution and once YOu encounter the first trial solution, show your process to fathom unnecessary nodes (simply cross-out all nodes that can be eliminated). Job P(u) P(4) P(I) P(2...
5 answers
For the following exercises, find $d y / d x$ at the value of the parameter.$$x=sqrt{t}, quad y=2 t+4, quad t=9$$
For the following exercises, find $d y / d x$ at the value of the parameter. $$ x=sqrt{t}, quad y=2 t+4, quad t=9 $$...
1 answers
Graph the following greatest integer functions. $$ k(x)=\left[\left[\frac{1}{2} x\right]\right] $$
Graph the following greatest integer functions. $$ k(x)=\left[\left[\frac{1}{2} x\right]\right] $$...
1 answers
If $f(x)=\sqrt{2 x+3}$ and $g(x)=\sqrt[3]{x-8},$ find the following function values. $$g(-19)$$
If $f(x)=\sqrt{2 x+3}$ and $g(x)=\sqrt[3]{x-8},$ find the following function values. $$g(-19)$$...
5 answers
Bentnen ouleban 044910Pant AMnal nlociron cunoni (nna Ihtoxigh 0-4ITL-dameler Iron 4a 0,014 V /m elacue Iala?ErnronyntpetelectronaecondAvallnnlotrunieAEd1.02 < 10clectron /
bentnen ouleban 044910 Pant A Mnal nlociron cunoni (nna Ihtoxigh 0-4ITL-dameler Iron 4a 0,014 V /m elacue Iala? Ernro nyntpet electrona econd Avallnnlotrunie AEd 1.02 < 10 clectron /...
5 answers
In the Winter In North Dakota much of the snow on the flelds disappears wlthout the snow ever melting This is an example of: (1 pt) boiling sublimation d. deposition_ Freezing
In the Winter In North Dakota much of the snow on the flelds disappears wlthout the snow ever melting This is an example of: (1 pt) boiling sublimation d. deposition_ Freezing...
5 answers
According to one pollster; 45% of children are afraid of the dark Suppose that a sample of size 23 is drawn: Find the value of v the standard deviation of the distribution of sample proportions.Write only a number as your answer: Round to two decimal places (for example: 8.21).
According to one pollster; 45% of children are afraid of the dark Suppose that a sample of size 23 is drawn: Find the value of v the standard deviation of the distribution of sample proportions. Write only a number as your answer: Round to two decimal places (for example: 8.21)....

-- 0.018867--