Solved: Consider n independent trials, each of which
Chapter , Problem 50(choose chapter or problem)
Consider n independent trials, each of which results in any of the outcomes i, i = 1, 2, 3, with respective probabilities p1, p2, p3, _3i =1 pi = 1. Let Ni denote the number of trials that result in outcome i, and show that Cov(N1,N2) = np1p2. Also explain why it is intuitive that this covariance is negative. (Hint: For i = 1, . . . , n, let Xi = _ 1 iftriali results in outcome 1 0 iftriali does not result in outcome 1 Similarly, for j = 1, . . . , n, let Yj = _ 1 iftrialj results in outcome 2 0 iftrialj does not result in outcome 2 Argue that N1 = _n i=1 Xi , N2 = _n j=1 Yj Then use Proposition 4.7.2 and Theorem 4.7.4.)
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer