1. In the accompanying table, the random variable x represents the number of tel
ID: 3174142 • Letter: 1
Question
1. In the accompanying table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability distribution, find its mean and standard deviation.
If the table is a probability distribution, what is its mean? Select the correct choice below and fill in any answer boxes within your choice.
A. Its mean is__? (Round to the nearest tenth as needed.)
B. The table is not a probability distribution.
If the table is a probability distribution, what is its standard deviation? Select the correct choice below and fill in any answer boxes within your choice.
A. Its standard deviation is___? (Round to the nearest tenth as needed.)
B. The table is not a probability distribution.
X P(x) 0 0.02 1 0.12 2 0.32 3 0.28 4 0.14 5 0.12Explanation / Answer
Mean, E(X) = 0 * 0.02 + 1 * 0.12 + 2 * 0.32 + 3 * 0.28 + 4 * 0.14 + 5 * 0.12
= 2.76 or 2.8 (ans)
E(X2) = 02 * 0.02 + 12 * 0.12 + 22 * 0.32 + 32 * 0.28 + 42 * 0.14 + 52 * 0.12
= 9.16
Var(X) = E(X2) - (E(X))2
= 9.16 - 2.762
= 1.5424
standard deviation = sqrt(1.5424) = 1.24 or 1.2 (ans)
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