Question

Find the mean, variance, and standard deviation of the random variable having the probability distribution given...

Find the mean, variance, and standard deviation of the random variable having the probability distribution given in the following table. (Round your answers to four decimal places.)

Random variable, x -7 -6 -5 -4 -3
P(X = x) 0.13 0.16 0.4 0.15 0.16
Math   Statistics-And-Probability   
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Answer #1

Solution :

x P(x) x * P(x) x2 * P(x)
-7 0.13 -0.91 6.37
-6 0.16 -0.96 5.76
-5 0.4 -2 10
-4 0.15 -0.6 2.4
-3 0.16 -0.48 1.44
Sum 1 -4.95 25.97

Mean = X * P(X)

= -4.95

Variance

= X 2 * P(X) - 2

= 25.97 - (-4.95)2 = 1.4675

Standard deviation = = 1.2114

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