Question

Let X equal the number of alpha particle emissions of carbon-14 that are counted by Geiger counter each second. Assume that the distribution of X is Poisson with mean 16. Let W equal the time in seconds before the seventh count is made. 1. Give the distribution of W. 2. Find (P(W\leq 0.5)).

Answer 1

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Answer 2

a) mean 16 means λ=16, hence θ=1/λ=1/16
see the attachment for distribution
b) first off, we need P(W>0.5) = −0.5/θ=e^−8=0.000335 then P(W≤0.5)=1−P(W>0.5)=1−0.000335=0.99965