Question

the table below shows the probability distribution of a random variable z.

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 mean \(\mu\) of a discrete probability distribution is given by \(\mu=\sum_{i}z_iP(z_i)\), where \(z_i\) are the values of the random variable and \(P(z_i)\) are their corresponding probabilities.

Step2: Calculate each term \(z_iP(z_i)\)

• For \(z = - 1\) and \(P(z)=0.13\): \((-1)\times0.13=-0.13\)
• For \(z = 0\) and \(P(z)=0.16\): \(0\times0.16 = 0\)
• For \(z = 1\) and \(P(z)=0.39\): \(1\times0.39=0.39\)
• For \(z = 2\) and \(P(z)=0.08\): \(2\times0.08 = 0.16\)
• For \(z = 3\) and \(P(z)=0.2\): \(3\times0.2=0.6\)
• For \(z = 4\) and \(P(z)=0.04\): \(4\times0.04 = 0.16\)
• For \(z = 5\) and \(P(z)=0\): \(5\times0=0\)

Step3: Sum up all the terms

\(\mu=-0.13 + 0+0.39+0.16+0.6+0.16+0\)

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Answer:

\(1.18\)