Problem 2E

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).

Answer:

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

G(w) =

Our goal is to find

The constant a and

Then the gompertz distribution function is

G(w) =

0.0953

or

G(w) =

We know that

G(64)-G(63) =

After substituting we get the answer.

a =

a = 0.00002646

Therefore constant a = 0.00002646

Then we have determine the .

=

= 0.0217

Therefore = 0.0217.