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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.

The table below shows the probability distribution of a random variable Z z PZ 11 006 10 004 9 052 8 011 gt 005 6 003 5 019 What is the expected value of Z Writ class=

Respuesta :

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

[tex]E(z)=\sum ^{\square}_{\square}z\cdot P(z)[/tex]

Substituting with the values from the table:

[tex]\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}[/tex]