Suppose N is a Poisson random variable with mean A. Show that E (1+ for any constant a. +a)^

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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?
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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