Question

objective 1
introduction
objective 2
objective 3
objective 4
objective 5
objective 6
6.1 discrete random variables
preparing for section 6.1
objective 4: compute and interpret the mean of a discrete random variable
part 1 of 2
0 of 1 point
in the probability distribution to the right, the random variable x represents the number of marriages an individual aged 15 years or older has been involved in. compute and interpret the mean of the random variable x.
type an integer or a decimal. do not round.)
μx = marriages

Explanation:

Step1: Recall the formula for the mean of a discrete random variable

The formula for the mean \(\mu_X\) of a discrete random variable \(X\) is \(\mu_X=\sum_{x}x\cdot P(x)\)

Step2: Calculate each term \(x\cdot P(x)\)

• When \(x = 0\), \(x\cdot P(x)=0\times0.271 = 0\)
• When \(x = 1\), \(x\cdot P(x)=1\times0.575=0.575\)
• When \(x = 2\), \(x\cdot P(x)=2\times0.121 = 0.242\)
• When \(x = 3\), \(x\cdot P(x)=3\times0.027=0.081\)
• When \(x = 4\), \(x\cdot P(x)=4\times0.005 = 0.02\)
• When \(x = 5\), \(x\cdot P(x)=5\times0.001=0.005\)

Step3: Sum up all the terms

\(\mu_X=0 + 0.575+0.242 + 0.081+0.02+0.005\)
\(\mu_X=0.923\)

Answer:

\(0.923\)