The conditional probability function for the random variables X and Y is 0 P(Y/X) = x0 [0.9 10.1 y 1 2 0.1 0 0.8 0.1 2 0 0.1 0.9. With P(x=0)=0.2, P(x-1)=0.4. Find P(X,Y), Hx, My, E(XY), OXY.
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- The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 32x²e-4x The kinetic energy of the particle is Y = 1/mX². Suppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.) x >0.Let X be a random variable with mean E[X] = 20 and variance Var(X) = 3. Define Y = 3 – 6X. Calculate the mean and variance of Y.4. Suppose that X has pdf f(x) = 3x² for 0 < x< 1. Find the pdf of the random variable Y = VX.
- Q3. The moment generating function for a random variable X is M(t) = e³t 1-t2¹ What are the mean and the variance of X, respectively? -1 < t < 1.Let X be a discrete random variable with P(X = -1) = .3, P(X = 1) = .45, P(X = 2) = .15 and P(X = 6) = .1. Find E(X).Suppose Y - Uniform(01,02) where the parameters and 02 take the values -4 and 6 respectively. Compute the probability P(Y < y) when y=0.00.
- Let X be a discrete random variable with P(X = -1) = .3, P(X = 1) = .45, P(X = 2) = .15 and P(X = 6) = .1. Find Var(X).Please find both c and dFor what values of k canf(x) = (1 − k)kx serve as the values of the probability distribution of arandom variable with the countably infinite range x =0, 1, 2, ...?
- Q2. Let X be a random variable with (a) Find E(X) (b) Find M(t). (0.42 f(x)=0.46 0.12 if x = 0 if x = 1 if x = 2Let X be a random variable with E[X]=2, Var(X)= 4. Compute the expectation and variance of 3–2X.Let X be a random variable with E[X] = 0 and Var(X) = 8. Let Y = 3X + 7. 1. Find the expectation E[Y] of Y. 2. Find the variance Var (Y) of Y. (E[Y], Var(Y)) = ¯¯¯).