Question

Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.) x −41 −27 −8 −3 P(X = x) 0.29 0.35 0.21 0.15

Answer 1

Answer:

a) Mean is -23.47

b) Variance is 206.59

c) standard deviation is 14.37

Step-by-step explanation:

Given that;

 x              −41        −27        −8         −3

P(X = x)      0.29      0.35      0.21      0.15

X.P            -11.89     -9.45    -1.68     -0.45

a) mean

Mean = ∑X.P = -11.89 +  -9.45 + -1.68 + -0.45

Mean = -23.47

b)  the variance

E(x²) = ∑x²P(X=x)

= (−41²×0.29) + (−27²×0.35) + (−8²×0.21) + (−3²×0.15)

= 487.49 + 255.15 + 13.44 + 1.35

= 757.43

So

Var(X) = E(x²) - [∑X.P]²

Var(X) = 757.43 - [-23.47]²

= 757.43 - 550.8409

= 206.5891 ≈ 206.59

Therefore Variance is 206.59

c) standard deviation

standard deviation SD(X) = √Var(X)

SD(X) = √206.5891

= 14.3732 ≈ 14.37

Therefore standard deviation is 14.37