Question

The table below shows the probability distribution of a random variable Z. Z P(Z) -13 0.69-12 0.18 -11 0.04 -10 0.01 -9 0.01 -8 0.04 -7 0.03 What is the expected value of Z? Write your answer as a decimal.

Answer 1

To be able to get the expected value of Z, we will be using the following formula:

`\text{ Expected Value = }\mu=Z_1P_1+Z_2P_2+Z_3P_3\text{ + }\ldots Z_nP_n`

We get,

`\text{ Expected Value = }\mu=Z_1P_1+Z_2P_2+Z_3P_3\text{ + }\ldots Z_nP_n`
`\text{ = (-13)(0.69) + (-12)(0.18) + (-11)(0.04) + (-10)(0.01) + (-9)(0.01) + (-8)(0.04) + (-7)(0.03)}`
`\text{ = (-8.97) + (-2.16) + (-0.44) + (-0.1) + (-0.09) + }(-0.32)\text{ + (-0.21)}`
`\text{ = -8.97 - 2.16 - 0.44 - 0.1 - 0.09 }-0.32\text{ - 0.21}`
`\text{ Expected Value = }\mu\text{ = -12.29}`

Therefore, the expected value of Z is -12.29.