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Probability-Distribution Questions
Probability-Distribution Questions
Let X equal the larger outcome when a pair of 6-sided dice are rolled.
Help with Pascal’s triangle and binomial coefficients
Let X be a discrete random variable with probability function f(x). Prove that E[a + b g(X) + c h(X)] = a + bE[g(X)] + cE[h(X))], where g and h are functions, and a, b and c are constants.
Let a random variable X have the p.f. f(x) = c(|x| + 1)2 for x = 0, ±1. Find the constant c so that f(x) is a valid probability function. Then, find E(X), E(X2 ) and var(X).
Uniform Distribution
Derive the probability distribution of the 1-year HPR on a 30-year US Treasury bond with a coupon of 3.0%. If it is currently selling at par and the probability distribution of its yield to maturity a year from now is as shown in the table below. (Assum
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