Question: 6. Let X be a continuous random variable with probability density function f (x ) = be-bx, x>0 ; b>0 elsewhere Find the moment generating

6. Let X be a continuous random variable with probability density function f (x ) = be-bx, x>0 ; b>0 elsewhere 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. M x (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) = (1-25001) 4 Determine the standard deviation of the claim size for this class of accidents

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