(Lamperti20) An urn contains exactly 5000 balls, of which an unknown number X are white and the rest red, where X is a random variable with a probability distribution on the integers 0, 1, 2, , 5000 (a) Suppose we know that E(X) Show that this is enough to allow us to calculate the probability that...

a The expected value of X is The probability that a white ball is drawn is Thus Thus 5 ...

(Lamperti20) An urn contains exactly 5000 balls, of which an unknown number X are white and the...

Question:

(Lamperti20) An urn contains exactly 5000 balls, of which an unknown number X are white and the rest red, where X is a random variable with a probability on the integers 0, 1, 2, . . . , 5000.
(a) Suppose we know that E(X) = μ. Show that this is enough to allow us to calculate the probability that a ball drawn at random from the urn will be white.
What is this probability?
(b) We draw a ball from the urn, examine its colour, replace it, and then draw another. Under what conditions, if any, are the results of the two drawings independent; that is, does P (white, white) = P (white)2 ?
(c) Suppose the variance of X is σ2. What is the probability of drawing two white balls in part (b)?
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...