Question

find the expected value (μ) of the random variable with the given probability distribution. μ = do not round your answer.

Explanation:

Step1: Recall the formula for expected value

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

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

• For \(x = 0\): \(0\times0.08=0\)
• For \(x = 1\): \(1\times0.12 = 0.12\)
• For \(x = 2\): \(2\times0.22=0.44\)
• For \(x = 3\): \(3\times0.24 = 0.72\)
• For \(x = 4\): \(4\times0.18=0.72\)
• For \(x = 5\): \(5\times0.16 = 0.8\)

Step3: Sum up the terms

\(\mu=0 + 0.12+0.44 + 0.72+0.72+0.8\)

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Answer:

\(2.8\)