In the accompanying table, the random variable x represents the number of televi

Question

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.

x,P(x)

0,0.03

1,0.14

2,0.24

3,0.27

4,0.18

5,0.14

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.

Its mean is _______?

OR

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.

standard deviation is _______?

OR

The table is not a probability distribution.

Explanation / Answer

Consider:

it is a probability distirbution, as the probabilities sum up to 1.

Thus,      
      
E(x) = Expected value = mean =    2.85   [ANSWER]

Var(x) = E(x^2) - E(x)^2 =    1.7875  

s(x) = sqrt [Var(x)] =    1.336974196   [ANSWER]
      

x P(x) x P(x) x^2 P(x) 0 0.03 0 0 1 0.14 0.14 0.14 2 0.24 0.48 0.96 3 0.27 0.81 2.43 4 0.18 0.72 2.88 5 0.14 0.7 3.5

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