find the expected value of the winnings from a game that has the following payout probability distribution…

find the expected value of the winnings from a game that has the following payout probability distribution: payout ($) 0 1 2 4 8 probability 0.50 0.25 0.13 0.06 0.06 expected value = ? round to the nearest hundredth.

find the expected value of the winnings from a game that has the following payout probability distribution: payout ($) 0 1 2 4 8 probability 0.50 0.25 0.13 0.06 0.06 expected value = ? round to the nearest hundredth.

Answer

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 and $p_i$ are their corresponding probabilities.

Step2: Calculate the product for each pair

For $x_1 = 0$ and $p_1=0.50$, the product is $0\times0.50 = 0$. For $x_2 = 1$ and $p_2 = 0.25$, the product is $1\times0.25=0.25$. For $x_3 = 2$ and $p_3 = 0.13$, the product is $2\times0.13 = 0.26$. For $x_4 = 4$ and $p_4 = 0.06$, the product is $4\times0.06=0.24$. For $x_5 = 8$ and $p_5 = 0.06$, the product is $8\times0.06 = 0.48$.

Step3: Sum up the products

$E(X)=0 + 0.25+0.26 + 0.24+0.48=1.23$.

Answer:

$1.23$