Question

# A random variable x has the following probability distribution. Determine the standard deviation of x. x...

A random variable x has the following probability distribution. Determine the standard deviation of x.

 x f(x) 0 0.05 1 0.1 2 0.3 3 0.2 4 0.35

A random variable x has the following probability distribution. Determine the expected value of x.

 x f(x) 0 0.11 1 0.04 2 0.3 3 0.2 4 0.35

QUESTION 2

1. A random variable x has the following probability distribution. Determine the variance of x.

 x f(x) 0 0.02 1 0.13 2 0.3 3 0.2 4 0.35

Following table shows the calculations:

 x f(x) x*f(x) x^2*f(x) 0 0.05 0 0 1 0.1 0.1 0.1 2 0.3 0.6 1.2 3 0.2 0.6 1.8 4 0.35 1.4 5.6 Total 2.7 8.7

The standard deviation is

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 x f(x) x*f(x) 0 0.11 0 1 0.04 0.04 2 0.3 0.6 3 0.2 0.6 4 0.35 1.4 Total 2.64

The expected value is

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 x f(x) x*f(x) x^2*f(x) 0 0.02 0 0 1 0.13 0.13 0.13 2 0.3 0.6 1.2 3 0.2 0.6 1.8 4 0.35 1.4 5.6 Total 2.73 8.73

The variance is

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