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 2 4 8 10 probability 0.35 0.20 0.10 0.20 0.15 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 2 4 8 10 probability 0.35 0.20 0.10 0.20 0.15 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 $p_1=0.35$, the product is $0\times0.35 = 0$. For $x_2 = 2$ and $p_2 = 0.20$, the product is $2\times0.20=0.40$. For $x_3 = 4$ and $p_3 = 0.10$, the product is $4\times0.10 = 0.40$. For $x_4 = 8$ and $p_4 = 0.20$, the product is $8\times0.20=1.60$. For $x_5 = 10$ and $p_5 = 0.15$, the product is $10\times0.15 = 1.50$.

Step3: Sum up the products

$E(X)=0 + 0.40+0.40 + 1.60+1.50$. $E(X)=3.90$.

Answer:

$3.90$