Exercise 14 Page 866

We want to decide whether we should buy the stock based on the given information. To do so, we will calculate the expected value of the stock's increase or decrease. Let's recall the definition of expected value.

Expected Value

If $A$ is an action that includes outcomes $A_1,$ $A_2,$ $A_3,\dots$ and $\text{Value}(A_n)$ is a quantitative value associated with each outcome, the expected value of $A$ is given by $\text{Value}(A)=P(A_1)\cdot \text{Value}(A_1)+P(A_2)\cdot \text{Value}(A_2)+\dots$

In other words, it is what we get, when we add up all products of the possible stock's increase or decrease and their corresponding probabilities. Before we start calculating, let's convert the probabilities from percent to decimal notation for convenience.

	Distribution of Stock's Change
Stock's Change, $\text{Value}(A_i)$	$\$10$	$\text{-}\$5$
Probability, $P(A_i)$	$25\%=0.25$	$75\%=0.75$

Now, we can calculate all the products of the profits and their probabilities.

	Distribution of Stock's Change
Stock's Change, $\text{Value}(A_i)$	$\$10$	$\text{-}\$5$
Probability, $P(A_i)$	$0.25$	$0.75$
$P(A_i)\cdot \text{Value}(A_i)$	$0.25\cdot \$10=\$2.5$	$0.75\cdot (\text{-}\$5)=\text{-}\$3.75$

Finally, we can calculate the expected value by summing all values from the the last row. Let's do it! The expected value is equal to $\text{-}\$1.25,$ so we conclude that on average the stock is expected to decrease. Therefore, we should not buy the stock.