A student taking five courses keeps a record of the number of assignments due each day in all her courses. Over the course of the 60-day semester she finds on 20 days no assignments are due, on 15 days an assignment is due in one course, on 15 days an assignment is due in two courses, on 9 days an assignments is due in three courses and once during the semester she has an assignment due in 4 courses. If X is the number of assignments due on a day selected at random from the semester, find E(X).
Is $E ( X ) = 0 \cdot \frac { 1 } { 3 } + 1 \cdot \frac { 1 } { 4 } + 2 \cdot \frac { 1 } { 4 } + 3 \cdot \frac { 3 } { 20 } + 4 \cdot \frac { 1 } { 60 }$ the correct answer?

Question

Quizplus · Accepted Answer

The formula for expected value is $E(X) = \sum_{i=1}^n x_i p_i$, where $x_i$ is the value of the random variable $X$ and $p_i$ is the probability of $X$ taking on the value $x_i$. In this case, $X$ can take on the values 0, 1, 2, 3, and 4. The probability of $X$ taking on the value 0 is 20/60 = 1/3. The probability of $X$ taking on the value 1 is 15/60 = 1/4. The probability of $X$ taking on the value 2 is 15/60 = 1/4. The probability of $X$ taking on the value 3 is 9/60 = 3/20. The probability of $X$ taking on the value 4 is 1/60. Therefore, the expected value of $X$ is $E(X) = 0 \cdot \frac { 1 } { 3 } + 1 \cdot \frac { 1 } { 4 } + 2 \cdot \frac { 1 } { 4 } + 3 \cdot \frac { 3 } { 20 } + 4 \cdot \frac { 1 } { 60 }$.

A Student Taking Five Courses Keeps a Record of the Number