Question

Let X be a random variable which follows a Poisson distribution whose parameter is equal to 1 . Determine E (X | 4 <X <14).

Answer 1

The distribution here is given as:

The conditional expected value of X here is computed as:

This is computed here as:

The probabilities in the above expression here are computed as:

The probabilities thus are computed here as:

X	P(X = x)	xP(X = x)
5	0.003066	0.015328
6	0.000511	0.003066
7	0.000073	0.000511
8	0.000009	0.000073
9	0.000001	0.000009
10	0.000000	0.000001
11	0.000000	0.000000
12	0.000000	0.000000
13	0.000000	0.000000
	0.003660	0.018988

Therefore, the conditional expected value here is computed as:

Therefore 5.188238 is the required conditional expected value here.