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Commerce Questions
Let X be a normal random variable with mean µ, variance^2 , pdf and mdf
A random variable X is lognormal if ln X, the natural logarithm of X, is normally distributed. Find the mean and variance of a lognormal random variable with ln X ∼ N(µ, σ2 ). [Hint: consider using the mgf of the normal distribution.]
The Bernoulli random variable takes values 0 and 1, and has probability function f(x) = (p^x) [(1 − p)^(1−x)]
Let X be a Poisson random variable with mean λ
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).
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