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 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 \( z_{i}P(z_{i})\)

• For \( z=-15\) and \( P(-15) = 0.15\): \((-15)\times0.15=- 2.25\)
• For \( z=-14\) and \( P(-14)=0.14\): \((-14)\times0.14=-1.96\)
• For \( z=-13\) and \( P(-13)=0.28\): \((-13)\times0.28=-3.64\)
• For \( z=-12\) and \( P(-12)=0.02\): \((-12)\times0.02=-0.24\)
• For \( z=-11\) and \( P(-11)=0.19\): \((-11)\times0.19=-2.09\)
• For \( z=-10\) and \( P(-10)=0.03\): \((-10)\times0.03=-0.3\)
• For \( z=-9\) and \( P(-9)=0.19\): \((-9)\times0.19=-1.71\)

Step3: Sum up all the terms

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Answer:

\(-11.11\)