Question

Let X denote the number that
shows up when a fair die is rolled
Variance of X is
A 3.8
B 3.1
C 2.92
D 1​

Answer 1

Answer:

d part is the correct answer

Answer 2

C) 2.92

Given:

X = number that shows up when a fair die is rolled

Variance V(X) = E(X²) - E(X)²

X = {1,2,3,4,5,6}

P(X=1) = 1/6

P(X=2) = 1/6

P(X=3) = 1/6

P(X=4) = P(X=5)= P(X=6) = 1/6

Now, E(X) = ∑X.P₁(X)

E(X) = 1/6 [1+2+3+4+5+6]

E(X) = 1/6 [21]

E(X) = 3.5

E(X²) =  ∑X².P₁(X)

E(X²) = 1/6 [1²+2²+3²+4²+5²+6²]

E(X²) = 1/6 [1+4+9+16+25+36]

E(X²) = 15.1

∵  V(X) = E(X²) - E(X)²

∴  V(X) = 15.1 - 12.25

V(X) ≈ 2.92