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Form of the binomial PMF. Consider a binomial random
Chapter , Problem 9(choose chapter or problem)
Form of the binomial PMF. Consider a binomial random variable X with parameters n and p. Let k* be the largest integer that is less than or equal to (n + l)p. Show that the PMF px (k) is monotonically nondecreasing with k in the range from 0 to k* . and is monotonically decreasing with k for k k* .
Questions & Answers
QUESTION:
Form of the binomial PMF. Consider a binomial random variable X with parameters n and p. Let k* be the largest integer that is less than or equal to (n + l)p. Show that the PMF px (k) is monotonically nondecreasing with k in the range from 0 to k* . and is monotonically decreasing with k for k k* .
ANSWER:Step 1 of 2
It is given that, Consider a binomial random variable X with parameters n and p Let k be the largest integer that is less than or equal to.
We will consider the ratio and find when it is greater than or less than 1.
We have