Question

find the expected value for the random variable.

e(z)= (type an integer or a decimal.)

Explanation:

Step1: Recall the formula for expected value

The formula for the expected value \(E(z)\) of a discrete random variable is \(E(z)=\sum_{i}z_{i}P(z_{i})\)

Step2: Calculate each term \(z_{i}P(z_{i})\)

• For \(z = 9\) and \(P(z)=0.12\), \(9\times0.12 = 1.08\)
• For \(z = 12\) and \(P(z)=0.22\), \(12\times0.22=2.64\)
• For \(z = 15\) and \(P(z)=0.43\), \(15\times0.43 = 6.45\)
• For \(z = 18\) and \(P(z)=0.16\), \(18\times0.16=2.88\)
• For \(z = 21\) and \(P(z)=0.07\), \(21\times0.07 = 1.47\)

Step3: Sum up the terms

\(E(z)=1.08 + 2.64+6.45+2.88+1.47\)
\(E(z)=14.52\)

Answer:

\(14.52\)