The problems are from probability class.

The problems are from 400 level probability class but introductory course. Please specify the terms you use (if necessary) and explain each step of your solutions. If there is anything unclear in the problem, please tell me. Thank you very much.

Probability

In the game of Two-Finger Morra, 2 players show 1 or 2 fingers and simultaneously guess the number of fingers their opponent will show. If only one of the players guesses correctly he wins the amount (in dollars) equal to the sum of the fingers shown by him and by his opponent. If both players guess correctly or neither guesses ...continues

Probability : Games Won

1. Suppose that two teams play a series of games that ends when one of the teams has one i number of games. Suppose that each game played is, independently, won by team A with probability p. Find the expected number of games that are played when (a) i = 2 and when (b) i = 3. Show also in both cases that this number is maximized ...continues

If each juror acts independently and if 65% of the defendants are guilty, find the probability that the jury renders a correct decision. What % of defendants are convicted?

Suppose that it takes at least 9 votes from a 12-member jury to convict a defendant. Suppose the probability that a juror votes a guilty person innocent is 0.2. whereas the probability that the juror votes an innocent person guilty is 0.1. If each juror acts independently and if 65% of the defendants are guilty, find the probabi ...continues

Introductory Probability

1) Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner. Suppose that one of the teams is stronger than the other and wins each game with probability 0.6, independant of the outcomes of the other games. Find the probability that the stronger team wins the series in exactly i gam ...continues

Probability : Ordered and Non-ordered Sets, Sampling and Replacing

Suppose that a batch of 100 items contains 6 that are defective and 94 that are nondefective. If X is the number of defective items in a randomly drawn sample of 10 items from the batch, find (a) P{X=0} and (b) P{X>2} (Answer first if sampling with replacing, and then if sampling without replacing)

Probability :Distribution Function

If X has distribution function F, what is the distribution function of the random variable aX + B, where a and B are constants, and a is not equal to zero. *(Please see attachment for complete question)

Random Variables : Expected Values

Let X be a random variable having expected value (mu) and variance (sigma)^2. Find the expected value and variance of: Y = (X - mu)/(sigma). (See attachment for full question)

Introductory Probability - Let X be such that

Let X be such that P{X=1}= p = 1 - P{X = -1} Find c≠1 such that E...(See attachment for full question)

Probability

Please specify the terms you use (if necessary) and explain each step of your solutions. In the game of Two-Finger Morra, 2 players show 1 or 2 fingers and simultaneously guess the number of fingers their opponent will show. If only one of the players guesses correctly, he wins an amount (in dollars) equal to the sum of the ...continues