Question

suppose that you are offered the following \deal.\ you roll a six - sided die. if you roll a 2, 3, 4 or 5, you win $5. otherwise, you pay $10. a. complete the pdf table. list the x values, where x is the profit, from smallest to largest. round to 4 decimal places where appropriate. probability distribution table x - 10 5 0 p(x) 0.1667 0.6667 0.1667 b. find the expected profit. $ (round to the nearest cent)

Explanation:

Step1: Recall expected - value formula

The formula for the expected value $E(X)$ of a discrete - random variable is $E(X)=\sum_{i}x_ip_i$, where $x_i$ are the possible values of the random variable and $p_i$ are their corresponding probabilities.

Step2: Identify values from the table

We have $x_1 = - 10$, $p_1=0.1667$, $x_2 = 0$, $p_2 = 0.1667$, $x_3 = 5$, $p_3=0.6667$.

Step3: Calculate the expected value

\[

$$\begin{align*} E(X)&=x_1p_1 + x_2p_2+x_3p_3\\ &=(-10)\times0.1667+0\times0.1667 + 5\times0.6667\\ &=- 1.667+0 + 3.3335\\ &=1.6665\approx1.67 \end{align*}$$

\]

Answer:

$1.67$