Sorry, ignore the last part in the image, by mistake I considered that they are asking probability at x=0.25.
Correct ans of last part: f(x) = 2, 0 < X < 0.5, so fx(0.25) = 2
12. Let X and Y be independent random variables, where X has a uniform distribution on...
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter A= 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(X > 0.25) U (Y> 0.25)}? nd (c) What is the conditional distribution of X, given that Y =3? ur worl mple with oumbers vour nal to complet the ovaluato all...
The random variables X and Y are independent with exponential densities fx (x) = e-"u(x) (a) Let Z = 2X + and w =-. Find the joint density of random variables Z and W (b) Find the density of random variable W (c) Find the density of random variable Z The random variables X and Y are independent with exponential densities fx (x) = e-"u(x) (a) Let Z = 2X + and w =-. Find the joint density of random...
Let X and Y be independent random variables. Random variable X has a discrete uniform distribution over the set {1, 3} and Y has a discrete uniform distribution over the set {1, 2, 3}. Let V = X + Y and W = X − Y . (a) Find the PMFs for V and W. (b) Find mV and (c) Find E[V |W >0].
. Let Y and Z be independent uniform random variables on the interval [0,1]. Let X = ZY. (a) Compute E(XY). (b) Compute E(X).
4. Let Y and Z be independent uniform random variables on the interval [0,1]. Let X Z (a) Compute E(XTY). (b) Compute E(X).
Let Y1, Y2, ..., Yn be independent random variables each having uniform distribution on the interval (0, θ). (a) Find the distribution of Y(n) and find its expected value. (b) Find the joint density function of Y(i) and Y(j) where 1 ≤ i < j ≤ n. Hence find Cov(Y(i) , Y(j)). (c) Find var(Y(j) − Y(i)). Let Yİ, Ya, , Yn be independent random variables each having uniform distribu- tion on the interval (0, 6) (a) Find the distribution...
Let Y1, Y2, ..., Yn be independent random variables each having uniform distribution on the interval (0, θ) (c) Find var(Y(j) − Y(i)). Let Y İ, Y2, , Yn be independent random variables each having uniform distribu- tion on the interval (0,0) Let Y İ, Y2, , Yn be independent random variables each having uniform distribu- tion on the interval (0,0)
Let X and Y be independent exponential random variables with parameter 1. Find the joint PDF of U and V. U = X + Y and V = X/(X + Y)
2. Let X and Y be independent, standard normal random variables. Find the joint pdf of U = 2X +Y and V = X-Y. Determine if U and V are independent. Justify.
6. Let X, Y be independent random variables, each having Exponential(A) distribution. What is the conditional density function of X given that Z =