Question

A card is drawn from the pack of 52 cards. This experiment is repeated 10 times. The probability distribution is given below. Find the expected value.

Answer 1

Answer:

Expected value = 2.7

Step-by-step explanation:

The expected value of a probability distribution is given by the equation:

`E(x)\text{ = }\sum ^{}_{}xP(x)`
`E(x)=x_1P(x_1)+x_2P(x)+x_3P(x_3)+x_4P(x_4)`

From the table given:

`\begin{gathered} x_1=1,P(x_1)=1/10,x_2=2,P(x_2)=3/10,x_3=3,P(x)\text{ = 4/10} \\ x_4=4,P(x_4)\text{ = 2/10} \end{gathered}`

Substitute these values into the expected value formula

`\begin{gathered} E(x)\text{ = 1(}(1)/(10))+2((3)/(10))+3((4)/(10))+4((2)/(10)) \\ E(x)\text{ = 1(0.1)+2(0.3)+3(0.4)+4(0.2)} \\ E(x)\text{ = 0.1 + 0.6 + 1.2 + 0.8} \\ E(x)\text{ = 2.7} \end{gathered}`

The expected value of the probability distribution = 2.7