Problem 6. Suppose the moment generating function of a random variable, X, is Compute the third...
6. Suppose the moment generating function of a random variable X is My(t) = (1 – 2+)-3, fort € (-1/2,1/2) Use this to determine the mean and variance of X.
What is the moment generating function of the random variable Y = 2X + 1, where X has the pdf f(x) = x/2 , 0 < x< 2, zero elsewhere?
(1 point) Suppose that the moment generating function of a random variable X is My(t) = exp(4e – 4) and that of a random variable Y is My(t) = ( oer + 3)''. If X and Y are independent, find each of the following. (a) P{X + Y = 2} = (b) P{XY = 0} = (c) E[XY] = (d) E[(X+Y)?] =
Question 18: a) Compute the moment generating function, MGF, of a normal random variable X with mean µ and standard deviation σ. b) Use your MGF from part a) to find the mean and variance of X.
(6) (15 points) The moment generating function for a normal random variable N (17,0?) is given by M(t) =e(+rt). Given Y with pdf N (4,0%), show that, if X and Y are independent, then the random variable 2 = x + Y is normally distributed with variance o + oz and mean 41 + 12. Please state clearly which properties of the moment generating function you are using.
problem 3 and 4 please. 3. Find the moment generating function of the continuous random variable & such that i f(x) = { 2 sinx, Ox CT, no otherwise. 4. Let X and Y be independent random variables where X is exponentially distributed with parameter value and Y is uniformly distributed over the interval from 0 to 2. Find the PDF of X+Y.
Suppose that a random variable X has the moment generating function given by M(t) (1- 2t)-1 Find E(X) and V(X)
If the discrete random variable X has a moment generating function given by My(t) = (e'-1) Find E(X + 2x2) and Var(2X + 40).
Random variable X has MGF(moment generating function) gX(t) = , t < 1. Then for random variable Y = aX, some constant a > 0, what is the MGF for Y ? What is the mean and variance for Y ?
(1 point) If X is a random variable with moment generating function then and Var(X)