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

Question

contestada

Respuesta :

nuhulawal20 nuhulawal20 · Answer 1 · 2020-11-10T02:03:50+01:00

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