Mix and Match

For these matching exercises, Y is a binomial random variable with parameters n and p, X is a Poisson random variable with parameter λ and B1 and B2 are Bernoulli trials with probability of success p.

 1. Expression for the variance of Y (a) np
 2. Probability that the first trial B1 fails. (b) e−λ
 3. Expression for the mean of X (c) e−λλ2/2
 4. Probability that Y is zero (d) p
 5. Probability that X is 2 (e) 0
 6. Covariance between B1 and B2 (f) pn
 7. Expression for the expected value of Y (g) 1 − p
 8. The expected value of B1 (h) (1 − p)n
 9. Probability that Y is n (i) np(1 − p)
10. Probability that X is zero (j) λ


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