Question

the table below shows the probability distribution of a random variable z.

what is the expected value of z?
write your answer as a decimal.

Explanation:

Step1: Recall the formula for expected value

The formula for the expected value \(E(Z)\) of a discrete random variable \(Z\) is \(E(Z)=\sum_{i}z_{i}P(z_{i})\), where \(z_{i}\) are the values of the random variable and \(P(z_{i})\) are their corresponding probabilities.

Step2: Calculate each term

For \(z = - 13\) and \(P(-13)=0.08\), the term is \((-13)\times0.08=-1.04\).
For \(z=-12\) and \(P(-12) = 0.08\), the term is \((-12)\times0.08=-0.96\).
For \(z=-11\) and \(P(-11)=0.33\), the term is \((-11)\times0.33=-3.63\).
For \(z=-10\) and \(P(-10)=0.51\), the term is \((-10)\times0.51=-5.1\).

Step3: Sum up the terms

\(E(Z)=(-1.04)+(-0.96)+(-3.63)+(-5.1)\)

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Answer:

\(-10.73\)