Question

The random variable X has the Poisson distribution with parameter λ > 0. According
to Chebeyshev’s Theorem, P(s < X < 99) ≥ 3/4.
1. Determine the value of k in the Chebeyshev’s inequality.
2. Determine the value of s

Answer 1

Consider a binomial random variable X with parameters n = 100 and p = 0.1, and
let Y be a Poisson random variable with E(Y ) = 2. Suppose that V ar(X+3Y ) = 21.
1. Find E(X), V (X) and V (Y ).
2. Determine E(X + 3Y ) and deduce E[(X + 3Y )
2
].
3. Find Cov(X, Y ). Are X and Y independent ? Justify