5

Page 151,2.7.7.* Let X1,X2,X3 have the joint pdf f(xl, x2,x3) = 6,0 < x1 x2 < x3 < 1, = 0 elsewhere. Find the joint pdf of Y1 = X1/x2, Y2 = X2/X3,Y3 = X3 a...

Question

Page 151,2.7.7.* Let X1,X2,X3 have the joint pdf f(xl, x2,x3) = 6,0 < x1 x2 < x3 < 1, = 0 elsewhere. Find the joint pdf of Y1 = X1/x2, Y2 = X2/X3,Y3 = X3 and show that they are mutually independent

Page 151,2.7.7.* Let X1,X2,X3 have the joint pdf f(xl, x2,x3) = 6,0 < x1 x2 < x3 < 1, = 0 elsewhere. Find the joint pdf of Y1 = X1/x2, Y2 = X2/X3,Y3 = X3 and show that they are mutually independent



Answers

A discrete random variable has pdf f(x)=k(1/2)^x for x=1,2,3, and zero otherwise. Then k is given by

Hi I'm David and I'm here to have your answering your question. Now let me bring up your question here. Now in discussion, we consider the uniform distribution. And because X followed a uniform from 0 to 1, it means that the F X echo to one found the X between zero and one and now we will have Y. It will follow on the uniform again. But on into her from X up to one. And then in the pot a solution means then the F Y. You got to 1/1 minus X from the UAE on interval from X to one. Now in the part I we want to fight is X quite positively or negatively corrected. So if X he's big, this one means that the why it would be inside the bigger interval between X and one. Therefore in Winston, why is big as well? And I found this one will give us that would be the positive or girl tolerated. Mhm. And then next way we'll find a part pay where we have to find john dancing identity function on the X. And Y. You noticed that the that's the under one here taking it will be the F. Y given X. And recall you that the F. Why even the X. By formula? It would equal to the F X. Y. Which is the challenge city. And if anybody F. X. So therefore we can find the F X. Y. By multiplying the F X. With the F Y given X. And we should have here one times one, only one month X. And then we will have here X. It will be great. Uh go to zero a small including one will be one here. And that will be the turn and stay often the accent of Y. And now in the past, see when you find the expedition under why? So I'm the why it will be equal to E. Of the Y. Given the X. And then we can do expedition outside one more. It is called the tower expectation. And here the inside here expectations on the one given the X by formula. And uh the main on the uniform, it will be no one over the b minus A. So we will have, it will go to record you that we have this one, the mean on the X. It would echo do the one. So we can compute as well. So we can have a integral one, the X from 0 to 1. And then we have the X. Here. So we have here the X square our two from the ones who have here will be one of the two. And therefore we will have this one. Exactly B minus with you. So they found the mean on the Y. Even the X. There we go to here. We have the one man is actually money by two. And as a result we have this a. Here. The inside must be the 1 -1 are with you. And for this expectation we can bring the half outside inside we have the I am the one minus X, and we should have one of the two, and then we have the one minister A X. So we have here one half, one month. I am the X. You get equal to a half. So therefore we have here a half times 2.5 an equal to one over fall. And this would be the minimum that why?

For the first parts E. We have, let's say F of X. Y. Is a joint si joint density function. Same city function. So we know that the double in Seeger or add squared. You have the function F. Of X. Y. The A. To be equal to one. So since f of eggs way You call it zero outside the red triangle. A size zero one 02 It's in place that the W. C. Girl X. Y. The A. It's equal to then see Gloria from negative infinity to infinity negative infinity to infinity. You have F. X. Y. The Y. The eggs to be equal to From zero. It's 1 0 to 2 of C. X. Mhm. One plus Y. The Y. The eggs. So we want to find a constant C. So this is equal to see you have The integral from 0 to 1 eggs. Just to give us Y plots one divided by two Y squared the interval from 0 to 2 the eggs. And this is equal to see named Tiger From 0 to 1. We have four eggs. The ace. This is equal to see you have two X squared from 0 to 1. Which is equal to to see. So then this implies that to see From here it's equal to one. So this like therefore C will be equal to one. Would be equal to one divided by two. So that's the constance then for the second parts be. So for B we have p eggs you have eggs greater than one. Why greater greater than or equal to when. So it is is equal to the integral to From Negative Infinity to one. From Negative Infinity to one. You have F. X. Y. The way the whitey eggs and this is equal to 0-1. You have 0-2. one divided by two eggs, one bloods way the Y. The eggs. So it is to give us the integer from 0 to 11 divided by two eggs. We have white platz one divided by two Y squared 0 to 2. And this will give us the eggs the integer from 0 to 1. We have one divided by two eggs. They this will give us three divided by soon The eggs. So if you integrate this you have three divided by four mm one. So three divided by four. You have one divided by two X squared the interval from service to one. This is called Sue to be divided by eight which is approximately three points 375 Then for the 3rd c. So footsie, we have he you have X plus Y. To be greater than or equal to one. And this is equal to be Yeah. X way in the indeed where the is uh triangle? A reaching triangular region. So we have P. Exploits why to be greater than or equal to one. To be equal to the N. C. Where From 0 to 1 0-1 minutes eight. We have one divided by two eggs. One plots way the way the eggs. And this will give us the interior from 0 to 1. We have one divided by two eggs way plus one divided by two Y squared The interval from 0-1. My next eggs the eggs. And this is equal to the integer from 0 to 1. You have one divided by two X. Then one divided by two X squared minus two eggs Plus three divided by two the eggs. So this will give us one divided by four X. To the power for divided by full. My next four divided by three is cube glass. We divided by two x. Grade The interval from 0 to 1 and this is equal to five, divided by 48 which is approximately 0.104 soon. That's an answer.

I am David. And I'm here to have you answering your question. Now let me bring up your question here in this question. We will reveal about the total probability. Reckon Yoda if we have the total probability for any X. It must echo to exactly will be one. So in this question were given the F. X. Echo to pay. Looks like we have to try and then times X. I'm not sure about this. So I will assume that. And now ex every co 212 and three. So let's try to make a table. I'm the probability now. So actually 212 and three now they're probably to get the one we put the one inside here and then we have will be 12 K. And found the probability to get a jew from the act we wanted to hear and I got a 25 day And the last one it will be three in San Ghana 36 gay. And remember that we end up everything that thought probability. There we go. To the 12 game plus 24 game plus 36 K. Exactly equal to one. So if we simplify this one we have the 12 plus 25 36 equals 72 K. Equal to one. Listen tells us that the K. Equity one number 72 that's gonna be the case. We're looking for

Hi I'm David and I'm here helping you answering your question. So let me bring up your question now. Okay. And now in this question when we discuss about the B. D. F. Of the function and were given the function F. X. X. Over two. Okay we understand. Is that correct? Will be one armor to power X. And we have the access go to 12 and three and then we go to zero otherwise. So here we're going to find a balance on the guy. Notice that the submission of the probability on the X. Echo two I for volume the I must echo to exactly what you want. So let me try to find the probability of the extra co 21 1st. So it changes that we go to the K And then one hour to power one and exactly it got you. OK Times one of it you and now when the probability X equal to two who have gay times one over to our two and we get equal to K. Times one over far and the last one probability exited three. Get negative. Okay times one over to our three. And we get to go to the gate terms 1 # eight now and we want to lie that we end them up. So toto you need to compute the sum here. So when we end them up we see the cable with a common factor inside. We have one of the two plus one of the four plus one of eight. And if we compare this one we'll have 1/2 +14 plus one of eight. We get equal to the seven out of eight. And we want this one exactly echo to one. So it means that came as Echo to the eight out of seven and this will be the value we are looking for.


Similar Solved Questions

5 answers
MatchMatchPrize Jackpot S1,000,000 S10,000 Sso0 Sz00 S10 S10 54 52 Overall chances of winning any prize:Chances 1in 302,575,350 1in 12,607,306 1 in 931,001 1in 38,792 1in 14,547 1in 606 1in 693 1in 89 1in 37 1in 24
Match Match Prize Jackpot S1,000,000 S10,000 Sso0 Sz00 S10 S10 54 52 Overall chances of winning any prize: Chances 1in 302,575,350 1in 12,607,306 1 in 931,001 1in 38,792 1in 14,547 1in 606 1in 693 1in 89 1in 37 1in 24...
5 answers
3 What parameters of the circuit influence the processes of the capacitor charging and discharging?
3 What parameters of the circuit influence the processes of the capacitor charging and discharging?...
5 answers
Cl0| 0QueSTION 16 POint Which of the following aqueous solutions will have the highest boiling point?Select the correct answer below:Sm of sugarSm of NaclSm of glucoseSm of NazSO4Content uttrlbution
Cl0| 0 QueSTION 16 POint Which of the following aqueous solutions will have the highest boiling point? Select the correct answer below: Sm of sugar Sm of Nacl Sm of glucose Sm of NazSO4 Content uttrlbution...
5 answers
Which of the groups in figure 1.9 represent clades? Which groups do not represent clades? Explain your answers.
Which of the groups in figure 1.9 represent clades? Which groups do not represent clades? Explain your answers....
5 answers
Bntonl, C,zhje s2muld amio Iting *lut kadte Enn 4 4IIC,t persue #parebaak I0& Tor #hith jnsaxrlng {70 € *bip zoyl in 28 3 & o{ benzereCnna
Bntonl, C,zhje s2muld amio Iting *lut kadte Enn 4 4IIC,t persue #parebaak I0& Tor #hith jnsaxrlng {70 € *bip zoyl in 28 3 & o{ benzere Cnna...
1 answers
In cats, blood-type A results from an allele $\left(I^{\mathrm{A}}\right)$ that is dominant over an allele $\left(i^{\mathrm{B}}\right)$ that produces blood-type $\mathrm{B}$. There is no O blood type. The blood types of male and female cats that were mated and the blood types of their kittens follow. Give the most likely genotypes for the parents of each litter. TABLE CANT COPY
In cats, blood-type A results from an allele $\left(I^{\mathrm{A}}\right)$ that is dominant over an allele $\left(i^{\mathrm{B}}\right)$ that produces blood-type $\mathrm{B}$. There is no O blood type. The blood types of male and female cats that were mated and the blood types of their kittens follo...
5 answers
The admission fee at an amusement park is S1.50 for children and S4 for adults. On a certain day; 337 people entered the park, and the admission fees collected totaled 918.00 dollars. How many children and how many adults were admitted?Your answer is number of children equalsnumber of adults equals
The admission fee at an amusement park is S1.50 for children and S4 for adults. On a certain day; 337 people entered the park, and the admission fees collected totaled 918.00 dollars. How many children and how many adults were admitted? Your answer is number of children equals number of adults equal...
5 answers
[1/2 Points]DETAILSPREVIOUS ANSWERSSCALCET9 2.5.022.Explain why tha function ig discontinuous at the given number a (Seled all that epply:]Ix *Ifx =Jtn K(x) and ffx) are finite, but are not equal. #ea {4) is defined and Iim Rx) is Inlte, but they are not equal;Mm {x) does not axIsta0{4) Is undefined none cithe aboveSketch the graph ot the function:searel
[1/2 Points] DETAILS PREVIOUS ANSWERS SCALCET9 2.5.022. Explain why tha function ig discontinuous at the given number a (Seled all that epply:] Ix * Ifx = Jtn K(x) and ffx) are finite, but are not equal. #ea {4) is defined and Iim Rx) is Inlte, but they are not equal; Mm {x) does not axIsta 0{4) Is ...
5 answers
Footrest: For approximately what 24-in. desk on an adjustable chair without worker sits at a elbows clear the desktop? will the worker' percentage of a 50%-female workforce
footrest: For approximately what 24-in. desk on an adjustable chair without worker sits at a elbows clear the desktop? will the worker' percentage of a 50%-female workforce...
2 answers
...
5 answers
Score on last try of 5 pts. See Details for moreNext questian You ran refry this questior belcwFind the maximum and minirum values of the funclion f(2,u) r vsubject to 51? + 2y" = 30Maximum value=Minimum value
Score on last try of 5 pts. See Details for more Next questian You ran refry this questior belcw Find the maximum and minirum values of the funclion f(2,u) r vsubject to 51? + 2y" = 30 Maximum value= Minimum value...
5 answers
If you sample a population of flowers (R-red, r-white, R is dominant) and find the R allele has a frequency of 0.46, what are your expected genotype and phenotype frequencies assuming HWE? You actually count 1000 flowers and find that 300 are RR, 450 are Rr and 250 are rr. Use a chi square goodness-of- fit test to calculate the Chi square value: If the critical Chi square value is 3.841,is the population in HWE?
If you sample a population of flowers (R-red, r-white, R is dominant) and find the R allele has a frequency of 0.46, what are your expected genotype and phenotype frequencies assuming HWE? You actually count 1000 flowers and find that 300 are RR, 450 are Rr and 250 are rr. Use a chi square goodness-...
5 answers
At a certain distance from a charged particle, the magnitude ofthe electric field is 228 V/m and the electric potential is 7.1 kV.The electric charge on the particle is:
At a certain distance from a charged particle, the magnitude of the electric field is 228 V/m and the electric potential is 7.1 kV. The electric charge on the particle is:...
5 answers
Use the function f and thc glvcn rcal numbcr to fInd ((-1) (a). (HInt: See Example Mlan answer does not cxlst, enter DNE ) K(x) -x 3x -((-1)(-5) =
Use the function f and thc glvcn rcal numbcr to fInd ((-1) (a). (HInt: See Example Mlan answer does not cxlst, enter DNE ) K(x) -x 3x - ((-1)(-5) =...
5 answers
PetAlollawng ontha plrs acnonHz{g) , Fzte) 2HP(g). C6) "Filul CF,(6}, 2C(s) "E,E) Glllck637 LI 6ekl 1523Ucllate AH lolTuachnEuivleneCH(e) GF2(g) ICF {E) + AHF (e)Expiesb YDur answuor hilabjule'#ulicant liqurasApSicmnBquiclanmeancortect TryAqainJinemdie rendining
PetA lollawng ontha plrs acnon Hz{g) , Fzte) 2HP(g). C6) "Filul CF,(6}, 2C(s) "E,E) Glllck 637 LI 6ekl 1523U cllate AH lol Tuachn Euivlene CH(e) GF2(g) ICF {E) + AHF (e) Expiesb YDur answuor hilabjule' #ulicant liquras Ap Sicmn Bquiclanmea ncortect TryAqain Jinemdie rendining...

-- 0.022237--