# Question

Prove Proposition 2.1 when

(a) X and Y have a joint probability mass function;

(b) X and Y have a joint probability density function and g(x, y) ≥ 0 for all x, y.

(a) X and Y have a joint probability mass function;

(b) X and Y have a joint probability density function and g(x, y) ≥ 0 for all x, y.

## Answer to relevant Questions

Consider Example 4f, which is concerned with the multinomial distribution. Use conditional expectation to compute E[NiNj], and then use this to verify the formula for Cov(Ni,Nj) given in Example 4f. Use the conditional variance formula to determine the variance of a geometric random variable X having parameter p. An insurance company has 10,000 automobile policyholders. The expected yearly claim per policyholder is $240, with a standard deviation of $800. Approximate the probability that the total yearly claim exceeds $2.7 million. A die is continually rolled until the total sum of all rolls exceeds 300. Approximate the probability that at least 80 rolls are necessary. This problem refers to Example 2f. (a) For any given molecule, what do you think is the (limiting) probability that it is in urn 1? (b) Do you think that the events that molecule j, j ≥ 1, is in urn 1 at a very large time ...Post your question

0