Suppose that the length W of a man’s life does follow the Gompertz distribution with λ(w) = a (1.1)w = ae (ln 1.1)w . P(63 < W < 64) = 0.01. Determine the constant a and P(W ≤ 71 | 70 < W).
Step 1 of 1 :
Given the length of a man’s life is W.
is a gompertz distribution function.
Then the geometric distribution function is
Our goal is to find
The constant a and
Then the gompertz distribution function is
We know that
After substituting we get the answer.
a = 0.00002646
Therefore constant a = 0.00002646
Then we have determine the .
Therefore = 0.0217.