A random variable X has the discrete uniform distribution fx

A random variable X has the discrete uniform distribution f(x) = 1/m x = 1,2.....m Show that the moment generating function is MX(t)=e^t(1-e^tm)/m(1-e^t) Use MX(t) to find the mean and variance of X. Suppose X has a continuous uniform distribution f(x)={630x^4(l-x)4, 0 LE x LE 1 0, Otherwise Use Chebyshev\'s rule to bound the probability that X differs from its mean more than two standard deviations and compare to the actual probability. If X1 ,X2,X3 and X4 are (pairwise) uncorrelated random variables, each having mean 0 and variance 1, compute the correlations coefficient of X1+ X2 and X2 + X3; X1 + X2 and X3 + X4. The repair time (in hours) for a certain electronically controlled milling machine follows the density function f(x) = { 3xe^2x, x GE 0 0, Otherwise Determine the moment-generating function for X (MX (t)) and use this function to evaluate E(X) and V(X)?

Solution