7. (12 points) 1. Find the moment generating function for an exponentially distributed a random variable with a parameter ) = 2. il. When Ahmed plays a certain game against his friend, he wins with probability 0.60, loses with probability 0.10 while with a probability of 0.30 the games result in a draw. Assuming independence, compute the following: a. The probability that Ahmed's first win happens when he plays his third game. b. The probability that Ahmed's fifth win happens when he plays his eighth game. iii. Let X be a Gaussian distributed random variable (RV) with mean /x = 3 and variance of = 9. a. Evaluate P[X3 S -1] b. Define the RV Y in terms of the RV X as Y = - = X + =. Obtain an expression for the PDF of Y , fy (y), then sketch it while clearly marking important points. C. Evaluate P [Y 2=]