# Question: Consider Example 4f which is concerned with the multinomial distribution

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.

## Answer to relevant Questions

An urn initially contains b black and w white balls. At each stage, we add r black balls and then withdraw, at random, r balls from the b + w + r balls in the urn. Show that E[number of white balls after stage t] = (b + w / ...Let X be a normal random variable with parameters μ = 0 and σ2 = 1, and let I, independent of X, be such that P{I = 1} = 1/2 = P{I = 0}. Now define Y by In words, Y is equally likely to equal either X or −X. (a) Are X ...A.J. has 20 jobs that she must do in sequence, with the times required to do each of these jobs being independent random variables with mean 50 minutes and standard deviation 10 minutes. M.J. has 20 jobs that he must do in ...A person has 100 light bulbs whose lifetimes are independent exponentials with mean 5 hours. If the bulbs are used one at a time, with a failed bulb being replaced immediately by a new one, approximate the probability that ...On any given day, Buffy is either cheerful (c), so-so (s), or gloomy (g). If she is cheerful today, then she will be c, s, or g tomorrow with respective probabilities .7, .2, and .1. If she is so-so today, then she will be ...Post your question