X has the following probability distribution P(X): Compute the variance value of X.
A)1.58
B).955
C).912
D).625

Question

X has the following probability distribution P(X):  Compute the variance value of X.
A)1.58 
B).955 
C).912 
D).625

Quizplus · Accepted Answer

To compute the variance of X, we first need to find the expected value of X.

E(X) = Σ(x*P(X)) where the sum is taken over all possible values of X.

E(X) = (-2*0.2) + (0*0.4) + (2*0.4) + (4*0.2) = 1.6

Now, to compute the variance of X, we use the formula:

Var(X) = Σ[(x-E(X))^2 * P(X)] where the sum is taken over all possible values of X.

Var(X) = [(-2-1.6)^2*0.2] + [(0-1.6)^2*0.4] + [(2-1.6)^2*0.4] + [(4-1.6)^2*0.2] = 0.912

Therefore, the answer is choice C with a variance value of 0.912.

X Has the Following Probability Distribution P(X): Compute the Variance