X and Y are independent random variables, -{ex. y20 x>0 0, others' 0, others Let U=X+Y, V=X/(X+Y). Determine the joint density function of U and V. fx(x)= 19= {e fy(y)=
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- A random variable Y have a distribution with parameter a > 0 and y, > 0 if its density function is given by: (ay“ if y> yo fV) = ya+T (0, elsewhere i) Derive the mean of Y. Show all necessary steps. ay (a-2)(a-1)²' ii) Show whether or not that the variance of Y is ·Suppose you have two independent random variables X ~ Y ~ Exponential(A2), A1 > 0, d2 > 0. Find: Exponential(A1) and (a) The joint density function for (X,Y). (b) P( > 1). (c) P(X +Y > 1).The number X is chosen at random between 0 and 1. determine the density functions of the random variables V = X/(1 - X) and W = X(1 - X)
- Two non-negative random variables X and Y have a joint density function f(x, y) = re-*v +1) x > 0, y > 0 Find the correlation coefficient.6) The random variables X and Y have joint density f( x, y) = x2-y2 for 1< x, 1s y and f( x, y) = 0 otherwise. %3! Compute the joint density of U = X /Y and V = X Y.Let random variables X and Y have the joint pdf fX,Y (x, y) = 4xy, 0 < x < 1, 0 < y < 1 0, otherwise Find the joint pdf of U = X^2 and V = XY.
- The density function, ху fy(x, y) = f(x) =9 0, 0The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by ´2e-(x+2) x 2 0, y 20 fx,y(x,y)=| else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.3935 b. 0.606 c. 0.7772 d. 0.3669 e. 0.63181) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.Y has a density function + y, Osys1, Ry) = {7 0, elsewhere. Find the mean and variance of Y. (Round your answers to four decimal places.) E(Y) = V(Y) =A random variable Y have a distribution with parameter a > 0 and yo > 0 if its density function is given by: ´ayf f(y) = {ya+1 (0, if y > yo elsewhere ii) ayg (a-2)(a-1)2" Show whether or not that the variance of Y isThe random variable Y has probability density function fV) = k(y + y®). 0 2. Hence find P(;< Y <). iii) Find the variance of Y.SEE MORE QUESTIONS
