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 \(\mu=\sum_{i}(x_i\times P(x_i))\).

Step2: Calculate each term \(x_i\times P(x_i)\)

• For \(x = 0\): \(0\times0.11=0\)
• For \(x = 1\): \(1\times0.40 = 0.40\)
• For \(x = 2\): \(2\times0.28=0.56\)
• For \(x = 3\): \(3\times0.13 = 0.39\)
• For \(x = 4\): \(4\times0.05=0.20\)
• For \(x = 5\): \(5\times0.03=0.15\)

Step3: Sum up the terms

\(\mu=0 + 0.40+0.56+0.39+0.20+0.15\)
\(\mu=1.7\)

Answer:

\(1.7\)