Chapter 6.1, Problem 9E

a.

To determine

To construct: A table of the probability distribution of Y .

Explanation of Solution

Given:

Probability of wining the game is 0.25.

Amount of bet is 1.

Payoff for the game is $3.

Calculation:

Here, payoff is given as 3. If the game is won the payoff leads the decrease in bet. That is,

  $\begin{array}{c}\text{Pay off = }3-1\\ =2\end{array}$

Using the provided information, the probability distribution is:

X ($)	-1	2
Probability	1-0.25	0.75

Thus, the probability distribution is:

X ($)	-1	2
Probability	0.75	0.25

b.

To determine

To find: The expected value and interpret it

Answer to Problem 9E

The expected value is $-0.25$

Explanation of Solution

Calculation:

The expected value can be calculated as:

  $\begin{array}{c}\text{E}\left(X\right)\text{=}{\displaystyle \sum x\times P\left(x\right)}\\ =-1\left(0.75\right)+\left(2\right)\left(0.25\right)\\ =-0.25\end{array}$

The expected value is $-0.25$ .

The expected loss for each game is -0.25.