Question

the table below shows the probability distribution of a random variable x.
what is the mean of the probability distribution?
write your answer as a decimal.

Explanation:

Step1: Recall the formula for the mean of a probability distribution

The formula for the mean \(\mu\) of a probability distribution 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 \(x = 7\) and \(P(7)=0\): \(7\times0 = 0\)
• For \(x = 8\) and \(P(8)=0.2\): \(8\times0.2=1.6\)
• For \(x = 9\) and \(P(9)=0.6\): \(9\times0.6 = 5.4\)
• For \(x = 10\) and \(P(10)=0.2\): \(10\times0.2=2\)

Step3: Sum up the terms

\(\mu=0 + 1.6+5.4 + 2\)

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Answer:

\(9\)