The mode of a discrete random variable X with p.m.f. p(x) is that value x* for w

Question

The mode of a discrete random variable X with p.m.f. p(x) is that
value x* for which p(x) is largest (the most probable x value).

Consider X distributed poisson(lambda) ... and k positive integer>=1

a) Show that P(X = k-1) < P(X = k) if and only if k < lambda.

{Note:
{Be sure to prove both directions of the "if and only if" in the above!

Thus, the poisson distribution is unimodal, ...
... with the mode occuring at floor(lambda).

b) Show that if lambda is a positive integer then ...
... P(X = lambda) = P(X = lambda - 1).

Thus, if lambda is an integer then both lambda and lambda-1 are modes.

Explanation / Answer

i am unable to upload image of answer so i am sending u the link of answer...please go through it

https://drive.google.com/file/d/0B6-y3LStajLMUURKR2hKN1NQWDVzWWdSZlY1a2RUWEtBcS1n/view?usp=sharing

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.