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Suppose that the jpdf of the continuous random variables W and Z is given by f (w,2) = r(e? 3wz) for 0 < W < 1. 2 < ? where reis constant. Find Consider th...

Question

Suppose that the jpdf of the continuous random variables W and Z is given by f (w,2) = r(e? 3wz) for 0 < W < 1. 2 < ? where reis constant. Find Consider the jpdf f (z.y) = (Sry 22 +1) for 0 < * <3 1 <y < 5. Calculate P(re < Y) What is fx(z)? Write Cov(X,Y) in terms of the integrals required t0 calculate it. While You have to set Hp the integrals completely, Vou do not have t0 evaluate aY of them:

Suppose that the jpdf of the continuous random variables W and Z is given by f (w,2) = r(e? 3wz) for 0 < W < 1. 2 < ? where reis constant. Find Consider the jpdf f (z.y) = (Sry 22 +1) for 0 < * <3 1 <y < 5. Calculate P(re < Y) What is fx(z)? Write Cov(X,Y) in terms of the integrals required t0 calculate it. While You have to set Hp the integrals completely, Vou do not have t0 evaluate aY of them:



Answers

$$\text {Evaluate the iterated integrals}$$ $$\int_{1}^{4} \int_{z-1}^{2 z} \int_{0}^{y+2 z} d x d y d z$$

If we'll fix boy equals for exploiting the stool picks and to excess queer. My six See you get to four to two and four to find em. Oy and him. And in X m oy ik was what mix and in X equals what X minus one. Wait, am Oy is not equal to index the victor fields not conservative. The line integral is not independent Over. So see x a quick t boy, you quick he squared and minus two. It's smaller than record t It's more than equal to therefore the integral See, if d r equals Diggle or c Well, what ex boy minus two x NeeIix plus two x squared My ethics do you want with sequence in bigger or C the integral from negative too to well, 40 times he squared minus duty plus duty Square dynasty ditty equals then titular from negatives too to yeah eight tea party minus two t squared minus duty DT By integrating the equals two to tip or four minus to over three tea por three. When the STI squared from negative to to to that equals negative 32 or three. Thank you

The question says that we have to evaluate the hydrated integral which is integration from 0 to 2 into integration from 0 to 0 square into integration from 02 by minus zed of two weeks minus Y. D. X. Day by B Z. Now moving towards the solution for the given integral leg uh integrate with respect to X. So integration from 0 to 2 into integration from 0 to 0 square x square minus y X Limit goes from 0 to Y- his head day by Dessert. So this will be called to integration from 0 to 2 into integration from 0 to 0 square is a square minus by said integration day by desert. So now we will be solving in respect of why? So it will be equal to integration from 0 to 2. Why is that the square minus one by two by squares. That limit goes from zero to that. The square dessert which will be called to integration from zero to to that to the par four minus one by twos to the par five day said. Now solving with respect to shed you will get one x 5, he said, To the power five one by 12. Is it to the power six limit from 0 to 2. Putting this you will get started over five minus 64 by 12, which will be equal to 16 by five, 16 x 15. And this will be your answer. Thank you.

Were given an iterated integral and we were asked to evaluate this Integral the iterated integral is the integral from X equals or Z equals 0 to 2 integral from why equals zero to Z squared and integral from X equals zero two X equals y minus Z of function to X minus. Why dx dy y dizzy to evaluate first taking into derivative with respect to X So we get integral from 0 to 2 integral from zero z squared, uh, X squared minus x y they read from zero two y minus Z de y dizzy and substitute begin integral from 0 to 2 integral from zero to Z squared of y minus Z squared minus x times Sorry. Minus y minus z times Why the wide easy which simplifies to integral from 0 to 2 integral from zero to Z squared of Z squared minus y z can do this by factoring out of y minus dizzy and then simplifying the wide easy and then taking into derivative with respect toe Why season to grow from 0 to 2 of why Z squared minus one half Why squared, See evaluated from is your room to Z squared easy and evaluating this is need to grow from 0 to 2 of see to the fourth minus one half times Z to the fifth. Yeah, Dizzy. Take me anti derivative. With respect to Z, this is 1/5 seed. The fifth minus 1 12. See to the sixth from Z equals 0 to 2, substituting immediate 32 5th. Minus 64 12th in this simplifies to 16. 15th. Uh huh.


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