Chapter 12.4, Problem 18PPS

To determine

The expected number of upsets.

Answer to Problem 18PPS

The required expected value of the upset is 4.34375.

Explanation of Solution

Given:

The table is provided as:

  

Considering X as random variables shows the number of upsets.

The table is showing the calculations for the expected value:

Upsets, X	Probability, P( X = x )	xP(X=x)
0	0.03125	0
1	0.0625	0.0625
2	0.09375	0.1875
3	0.125	0.375
4	0.125	0.5
5	0.3125	1.5625
6	0.125	0.75
7	0.09375	0.65625
8	0.03125	0.25
Total		4.34375

Therefore, the expected number of the upsets are:

  $\begin{array}{c}E\left(\text{snow}\text{date}\right)={\displaystyle \sum xP\left(X=x\right)}\\ =4.34375\end{array}$

Thus, the required expected value is 4.34375.