Question

Suppose that the duration of unemployment can be accurately modeled by an exponential distribution. What is the probability that a person finds a job within 6 months (26 weeks) if the mean duration of unemployment is 20 weeks

Answer 1

Answer:

The answer is "0.7275".

Explanation:

6 months =26 weeks.

Since we can write pdf in a medium 20 weeks since the distribution is exponential

$P(X$

                 $= \frac{1}{20} \frac{e^{\frac{-x}{20}}}{\frac{-1}{20}}|_{0}^{26} \\\\\\ = -(e^{ \frac{-26}{20}} - e^{0})\\\\\\ = 0.7275$