Question

Consider the random variable, X, whose probabilities are given in this table. X P(X) 0 0.2373...

Consider the random variable, X, whose probabilities are given in this table.

X P(X)
0 0.2373
1 0.3955
2 0.2637
3 0.0879
4 0.0146
5 0.0010

What is the standard deviation of this probability distribution? Round to the nearest thousandth (three decimal places), if needed.

Math   Statistics-And-Probability   
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Answer #1

Solution:

x P(x) x * P(x) x2 * P(x)
0 0.2373 0 0
1 0.3955 0.3955 0.3955
2 0.2637 0.5274 1.0548
3 0.0879 0.2637 0.7911
4 0.0146 0.0584 0.2336
5 0.001 0.005 0.025
Sum 1 1.25 2.5

Mean = X * P(X)

= 1.25

Standard deviation =

=X 2 * P(X) - 2

=  2.5 - (1.25)2 = 0.9375

Standard deviation = = 0.968

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