Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The duration $Y$ of long-distance telephone calls(in minutes) monitored by a station is a random variable with the properties that $P(Y=3)=0.2$ and $P(Y=6)=0.1$ Otherwise,Y has a continuous density function given by $$ f(y)= \begin{cases} \tfrac{1}{4}ye^{-y/2},\quad y>0,\\ 0,\qquad\qquad\text{elsewhere}. \end{cases} $$

The discrete points at 3 and 6 are due to the fact that the length of the call is announced to the called in three minute intervals and the caller must pay for three minutes even if he talks less than three minutes. Find the expected duration of a randomly selected long distance call.

share|cite|improve this question
up vote 1 down vote accepted

Hint: Write $Y=Y\mathbf{1}_{\{0<Y<3\}}+3\mathbf{1}_{\{Y=3\}}+Y\mathbf{1}_{\{3<Y<6\}}+6\mathbf{1}_{\{Y=6\}}+Y\mathbf{1}_{\{Y>6\}}$.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.