Question

The table below shows the probability distribution of a random variable Z. z P(Z) -11 0.06 -10 0.04 -9 0.52 -8 0.11 -> 0.05 -6 0.03 -5 0.19 What is the expected value of Z? Write your answer as a decimal.

Answer 1

The expected value (E) of a random variable (z) is computed as follows:

`E(z)=\sum ^(\square)_(\square)z\cdot P(z)`

Substituting with the values from the table:

`\begin{gathered} E(z)=-11\cdot0.06-10\cdot0.04-9\cdot0.52-8\cdot0.11-7\cdot0.05-6\cdot0.03-5\cdot0.19 \\ E(z)=-0.66-0.4-4.68-0.88-0.35-0.18-0.95 \\ E(z)=-8.1 \end{gathered}`