Consider the binomial distribution P(k)= b(k; n, p). Show that: (n-k+ 1)p P(k) b(k; n, p) P(k-1) b(k-1; n, p) (i) kq 0. (ii) P(k) > P(k-1) for k<(n+1)p and P(k) < P(k-1) for k> (n+1)p. =

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Consider the binomial distribution P(k) = b(k; n, p). Show that:
(i)
(n-k+ 1)p
kq
0. (ii) P(k) > P(k-1) for k<(n+1)p and P(k) < P(k-1) for k> (n+1)p.
P(k)
b(k; n, p)
P(k-1) b(k-1; n, p)
1
Transcribed Image Text:Consider the binomial distribution P(k) = b(k; n, p). Show that: (i) (n-k+ 1)p kq 0. (ii) P(k) > P(k-1) for k<(n+1)p and P(k) < P(k-1) for k> (n+1)p. P(k) b(k; n, p) P(k-1) b(k-1; n, p) 1
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