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

The answer is "0.7275".

Step-by-step explanation:

6 months =26 weeks.

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

`P(X<26) =\int_(0)^(26) (1)/(20)e^{(-x)/(20)} dx \\\\`

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