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Find the mean, variance and standard deviation for the probability distribution given below. Give your answers...

Find the mean, variance and standard deviation for the probability distribution given below. Give your answers to at least 4 decimal places. X -4 3 9 11 P(X) 0.599 0.131 0.214 0.056 A. Mean = B. Variance = C. Standard Deviation =

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Expert Solution

Solution:

x P(x) X P ( x ) X2 P ( x )

4 0.599 2.396 9.584

3 0.131 0.393 1.179

9 0.214 1.926 17.334

11 0.056 0.616 6.776

1 5.331 34.873

A )Mean = =  x P (x )

= 5.331

Mean = =5.3310

B ) Variance  = 2 = x2 P (x ) - ( )2

2 = 34.873 - ( 5.331 )2

2 =  34.876 - 28.420

2 = 6.456

Variance=  6.4560

C ) Standard deviation =

   = x2 P (x ) - ( )2

= 34.873 - ( 5.331 )2

=  34.876 - 28.420

= 6.456

= 2.5409

The standard deviation = 2.5409

orchestra answered 2 years ago
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