Exercise 10.19 (Continuing Example 10.9). Repeat n times a trial with three outcomes 1,2,3 that appear with probabiliti...
Exercise 10.19 (Continuing Example 10.9). Repeat n times a trial with three outcomes 1,2,3 that appear with probabilities pi, p2, p3 with p p2 p3-1. Let Xi be the number of times outcome i appears in the n trials (a) Find the conditional joint probability mass function of (X2, X3), given Xim That is, find the probabilities nd the conditional joint probability mass tunction o P(X2k, X3-l|Xfor integers k, l. (b) Utilizing part (a, identify the conditional distribution ofXgiven X1- m.
Exercise 10.19 (Continuing Example 10.9). Repeat n times a trial with three outcomes 1,2,3 that appear with probabilities pi, p2, p3 with p p2 p3-1. Let Xi be the number of times outcome i appears in the n trials (a) Find the conditional joint probability mass function of (X2, X3), given Xim That is, find the probabilities nd the conditional joint probability mass tunction o P(X2k, X3-l|Xfor integers k, l. (b) Utilizing part (a, identify the conditional distribution ofXgiven X1- m.