Problem 4 (counts as two problems): Let X1, X2, ., X„be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). The following set of steps illustrates the Law of Large Numbers at work. Compute the mean and fV (which in fô-tcx, +x omnute themaan n ved in theninatnses of X.. c) Suppose n = 10,000. Use Chebyshev's inequality to provide an upper bound for the probability that the difference between p and p exceeds 0.05.

The mean (or expected value) of a probability distribution can be calculated by first making the probability distribution. Then multiply the possible values of the Random Variable by their probabilities (X*P(X)) then add all the X*P(X) up.  On the TI 83/84 calculator you can  1) Enter the values of the RV's into List 1 (Press STAT, 1 (for Edit), highlist L1 and press CLEAR if needed, then enter values into the list) 2) Enter the probabilities into L2 (press > and then enter the values in the list. highlight L2 and press CLEAR first if needed). 3) 2nd MODE (to quit the list) 4) STAT, > (for CALC), select 1-Var Stats, List: L1 (2nd 1), FreqList: L2 (2nd 2).  Then calculate.  x¯ is the expected value (mean) of the frequency distribution.    A game is played. If you win you gain $4. If you lose you lose $10. The probability of winning is 0.747.  What is the expected value (mean)?

When computer generates random digits, the probability that any particular digit in the set {0,1,2,... 9}is generated on any individual trial is 1/10 0.1. Suppose that we are generating digits one at a time and let X the number of digits that the computer generates to get the first zero. (a) Detemine the probability that the first 0 occurs on the fifth random digit generated_ (6) How many random digits would you expect to have to generate in order to observe the first 0? (c) Calculate and interpret the standard deviation of X.

1. Given that X~N(39,32)A Random variable X is normally distributed and has a mean of 9 C Random variable X is not normally distributed and the mean is 39 B Random variable X is normally distributed and has a mean of 3 D Random variable X is normally distributed and the mean is 39