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)

Introductory Probability Course at the 400 Level.

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 fingers shown by him and his opponent. If both players guess correctly or if neither guesses correctly, then no money is exchanged. Consider a specified player and denote by X the amount of money he wins in a single game of Two-Finger Morra. (a) If each playesr acts independently of the other, and if each player makes his choice of the number of fingers he will hol... click for more

Probability (Poisson Random Variable; Value; Variance)

1. Suppose that the number of eggs laid on a tree leaf by a particular type of insect is a Poisson random variable with l = 1. (a) What is the probability that any particular leaf will have at least two eggs? (b) Suppose that a person searches through leaves on a tree until he finds one with at least two eggs. Letting X = the number of leaves searched, what is the expected value and variance of X? *Please specify the terms you use (if necessary) and explain each step of your solutions.