Question: Letbe a random variable with the following probability distribution. Value X of X P(X=x) 0 0.10 10 0.35 20 0.15 30 0.25 40 0.15 (a)

Letbe a random variable with the following probability distribution.

Value X of X P(X=x)

0 0.10

10 0.35

20 0.15

30 0.25

40 0.15

(a) Find the expectation E(X)of X.

(b) Find the variance Var (X) ofX .

The workers' union at a certain university is quite strong. About 96% of all workers employed by the university belong to the workers' union. Recently, the workers went on strike, and now a local TV station plans to interview a sample of20 workers, chosen at random, to get their opinions on the strike.

(a) Estimate the number of workers in the sample who are union members by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Please do not round your response.

(b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Please round your response to at least three decimal places.

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