Let X equal the number of alpha particle emissions of carbon-14 that are counted by a Geiger counter each second. Assume that the distribution of X is Poisson with mean 16. LetW equal the time in seconds before the seventh count is made.

(a) Give the distribution of W.

(b) Find P(W ≤ 0.5). Hint: Use Equation 3.2-1 with λw = 8.

Step 1 of 3:

Given that X denotes the number of carbon particles emission of carbon-14 in each second and W denotes the time in seconds before the seventh count is made.

Also it is given that X has Poisson distribution with parameter 16. That is X~P(16).

We have to find the distribution of W and then using the given equation we have to find the required probability.

Step 2 of 3:

(a)

Here we have to identify the distribution of W.

W has a gamma distribution with parameter =7 and =,that is

Symbolically we can write it as W~G(=7, ).

Thus,

f(W)=

=

=