Question

The p.m.f. of an r.v. X is ______ 

P(x) = `{{:(x^2/"k"";", x = - 4"," - 3"," - 2"," - 1),(0";", "otherwise"):}`

Then, E(X) = ______ 

Options

• `-7/3`

• `-5/3`

• `-10/3`

• `-8/3`

Answer 1

The p.m.f. of an r.v. X is ______ 

P(x) = `{{:(x^2/"k"";", x = - 4"," - 3"," - 2"," - 1),(0";", "otherwise"):}`

Then, E(X) = `underline(-10/3)`

Explanation:

X = x	-4	-3	-2	-1
P(X = x)	`16/k`	`9/k`	`4/k`	`1/k`

Since, P(-4) + P(-3) + P(-2) + P(-1) = 1

∴ `16/k + 9/k + 4/k + 1/k = 1`

⇒ `30/k = 1`

⇒ k = 30

∴ E(X) = ∑x_i.P(x_i)

= `-4. 16/30 - 3. 9/30 - 2. 4/30 - 1. 1/30`

= `-100/30`

= `-10/3`