Question: Show that

a) b(x; n, q ) = b( n – x; n, 1 - q) ( Recall that b represents the probability distribution of a random variable with a binomial distribution)

If we define

\[B(x;n,\theta )=\sum\limits_{k=0}^{x}{b(k;n,\theta )}\] for x = 0,1,2,…..n, show that

b) b(x; n, q) = B(x; n, q) – B(x-1; n, q);

c) b(x; n, q) = B(n-x; n, 1 - q) – B(n- x – 1; n, 1 - q);