Question

find the expected value for the random variable x having the probability function shown in the graph. complete the probability distribution table below. (simplify your answers. type integers or decimals.)

Explanation:

Step1: Determine the probabilities from the graph

From the graph, we can see that \(P(4) = 0.35\), \(P(8)=0.25\), \(P(12) = 0.2\), \(P(16)=0.15\), \(P(20)=0.05\)

Step2: Calculate the expected value \(E(X)\)

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

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Answer:

The probability distribution table: \(P(4) = 0.35\), \(P(8)=0.25\), \(P(12) = 0.2\), \(P(16)=0.15\), \(P(20)=0.05\)

The expected value \(E(X) = 9.2\)