Find the probability density of the sum W = X+ Y.
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- The median of the random variable X whose probability density function 3 =x² ,0 < x < 2 - - f(y) = }2 ,0. W. is2x A random variable X has the density function f(x)= } k- 0, Otherwise. For what value of k the variance of X equal to 2.Let X and Y be two independent continuous random variables with the following probability density functions: f(x) = (1/2)e^(-x/2) for x > 0 g(y) = (1/3)e^(-y/3) for y > 0 What is the probability density function of Z = X + Y?
- Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)3. The probability density functions of two statistically independent random variables X and Y are fx(x) = }u(x – 1)e-tx-1)/2 fr(y) =u(y- 3)e-(s-3)/4 Find the probability density of the sum W =X+Y.A continuous variable Y has a probability density function for which the moment generating function is given by M(t)=e^(2*t+72*t^2). What is the variance of the variable, Var[Y]?
- 8. Let the probability density of the random variable ({, n) be f(x, y) = { ke-(2x+7y) x>0 y>o elsewhere Find (1) the constant k; (2) the distribution function of (§, n);let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x isThe probability density function of the random variable X whose moment generating function (-) (1 + e') is
- Let Y be a random variable with pdf f(y)= (1/18)(y^3−1) for 1<y<3.(a) Calculate P (Y > 2.5).(b) Calculate the variance of Y .The density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).The joint probability density function of two random variables X and Y is f(x, y)= 4xye^-(x^2+y^2). Find P(1<x<=2, 1<Y<=2)