Suppose N is a Poisson random variable with mean A. Show that E (1+ for any constant a. +a)^
Suppose N is a Poisson random variable with mean A. Show that E (1+ for any constant a. +a)^
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 2E
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![Suppose N is a Poisson random variable with mean A. Show that E (1+a)M=
for any constant a.
1.
(b) Telephone calls enter a switchboard in a Poisson process of rate A every 10 minutes. In
a 10 minute period, N calls enter the switchboard.
chance an unofficial tea-break, the operator wants to estimate the probability 0 that
there will be no incoming calls in the next 20 minutes, using this single observation
order to decide whether he can
N.
Write down an expression for 0 in terms of A. Use this, together with the result in
part (a), to suggest an unbiased estimator T(N) of 0. Is this estimator sensible?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0830e9a-739d-4340-85c7-70894ba6f956%2F6fa8065e-1665-4c1c-add3-44a4944b37d3%2Fhykf1f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose N is a Poisson random variable with mean A. Show that E (1+a)M=
for any constant a.
1.
(b) Telephone calls enter a switchboard in a Poisson process of rate A every 10 minutes. In
a 10 minute period, N calls enter the switchboard.
chance an unofficial tea-break, the operator wants to estimate the probability 0 that
there will be no incoming calls in the next 20 minutes, using this single observation
order to decide whether he can
N.
Write down an expression for 0 in terms of A. Use this, together with the result in
part (a), to suggest an unbiased estimator T(N) of 0. Is this estimator sensible?
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