# Thread: Conditional Expectation Problem

1. ## Conditional Expectation Problem

I have the solution to this example, but I don't understand it. It's the third step that I don't understand.

"For a population of individuals, you are given:

i) Each individual has a constant force of mortality.

ii) The forces of mortality are uniformly distributed over the interval (0,2).

Calculate the probability that an individual drawn at random from this population dies within a year."

Solution:

I don't understand the third step, where the integral is split. How is the f(u) function able to disappear and get replaced by 1/2. It's been a few months since I've done a multivariable probability problem...

2. Originally Posted by paulrb
I have the solution to this example, but I don't understand it. It's the third step that I don't understand.

"For a population of individuals, you are given:

i) Each individual has a constant force of mortality.

ii) The forces of mortality are uniformly distributed over the interval (0,2).

Calculate the probability that an individual drawn at random from this population dies within a year."

Solution:

I don't understand the third step, where the integral is split. How is the f(u) function able to disappear and get replaced by 1/2. It's been a few months since I've done a multivariable probability problem...
"The forces of mortality are uniformly distributed over the interval (0,2)" => $\displaystyle f_M(\mu) = \frac{1}{2}$. Uniform distribution: http://en.wikipedia.org/wiki/Uniform...on_(continuous)