Question

Let the p.m.f. of a random variable X be P(x) = `(3 - x)/10`, for x = −1, 0, 1, 2 = 0, otherwise Then E(x) is ______.

Options

• 1

• 2

• 0

• –1

Answer 1

Let the p.m.f. of a random variable X be P(x) = `(3 - x)/10`, for x = −1, 0, 1, 2 = 0, otherwise Then E(x) is 0.

Explanation:

Given the probability mass function `P(x) = (3-x)/10` for x ∈ {−1, 0, 1, 2}, we calculate the values as follows:

For x = –1:

`P(-1) = (3-(-1))/10 `

`=4/10`

= 0.4

For x = 0:

`P(0) = (3-0)/10`

`= 3/10`

= 0.3

For x = 1:

`P(1) = (3-1)/10`

`= 2/10`

= 0.2

For x = 2:

`P(2) = P(2) = (3-2)/10`

`= 1/10`

= 0.1

Now, calculate the expected value E(X):

E(X) = (–1 × 0.4) + (0 × 0.3) + (1 × 0.2) + (2 × 0.1)

E(X) = –0.4 + 0 + 0.2 + 0.2

E(X) = –0.4 + 0.4

E(X) = –0.4 + 0.4

E(X) = 0