Answer the following questions?

1. A die has three sides. Use formulas from class to nd the expected value, variance and standard deviation dxnxm (a) the number of tosses of the die until the rst 1: (b) the number of tosses of the die until the third 1; (c) the number of 1's in 8 tosses of the die. 2. Find the expected value and variance of a single toss of an n-sided die. 3. Let X be the result of tossing a die marked 2, 4, 4, 6, 6, 6 and then Y the result of tossing an X -sided die. Find (a) P144): ('3) E[Y]; (c) E[X]. 4. Let X = 0.1.2 with probabilities 1/7, 2/7 and 4/? respectively. (a) Find the moment generating function. (b) Use the moment generating function to nd E [X ] and E[X2]