1. Let X be the number of tails in the experiment of tossing a balanced coin 4 times. Find the distribution of Y = - 1 1 +X 2. Let Xhas the Poisson distribution with probability distribution function f (x ) = x = 0, 1,2,... x! to, elsewhere Find the distribution of Y = 4X . 3. If the probability density of X is given by f ( x ) = 12 ' 00 elsewhere ' ; b>0 Find the moment generating function of X, Mx(t) . Then, find M x (-6b) . 7. Let X be a random variable with probability distribution function 1/2 if x = 0 f (x) = 1 (1/2 ) e -x if x > 0 SMG 2013 Probability Find the moment generating function of X. 8. A random variable of X has the Poisson distribution p(x; ) = e "u* / x! for x =0,1,2,... with the following moment generating function. Mx (t) = e"(e'-1) Find the mean and variance of X. 9. An actuary determines that the claim size for a certain class of accidents is a random variables, X, with moment generating function. M x (1) = (1- 2500t) 4 Determine the standard deviation of the claim size for this class of accidents