Exercises
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 |
True/False
Mark each statement True or False. If you believe that a statement ...
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