Question

use the probability distribution or histogram to find the (a) mean, (b) variance, (c) standard deviation, and (d) expected value of the probability distribution, and (e) interpret the results. the histogram shows the distribution of household sizes in country a for a recent year
(a) the mean is
(type an integer or a decimal. do not round)

Explanation:

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

The formula for the mean \(\mu=\sum_{x}x\cdot P(x)\), where \(x\) is the value of the random variable and \(P(x)\) is the corresponding probability.

Step2: Calculate the product \(x\cdot P(x)\) for each \(x\)

• For \(x = 1\) and \(P(1)=0.276\), \(x\cdot P(x)=1\times0.276 = 0.276\)
• For \(x = 2\) and \(P(2)=0.335\), \(x\cdot P(x)=2\times0.335=0.67\)
• For \(x = 3\) and \(P(3)=0.152\), \(x\cdot P(x)=3\times0.152 = 0.456\)
• For \(x = 4\) and \(P(4)=0.131\), \(x\cdot P(x)=4\times0.131=0.524\)
• For \(x = 5\) and \(P(5)=0.068\), \(x\cdot P(x)=5\times0.068 = 0.34\)
• For \(x = 6\) and \(P(6)=0.030\), \(x\cdot P(x)=6\times0.030=0.18\)

Step3: Sum up the products

\(\mu=0.276 + 0.67+0.456+0.524+0.34+0.18\)

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Answer:

\(2.446\)