Question

A random variable X has the following probability distribution:

X = xi	1	2	3	4
P(X = xi)	0.2	0.15	0.3	0.35

The mean and the variance are respectively ______.

विकल्प

• 3.8 and 1.26

• 2.8 and 1.26

• 3.8 and 1

• 2.8 and 1

Answer 1

A random variable X has the following probability distribution:

X = xi	1	2	3	4
P(X = xi)	0.2	0.15	0.3	0.35

The mean and the variance are respectively 2.8 and 1.26.

Explanation:

Mean = E(X) = `sum x_"i""P"(x_"i")`

= 1(0.2) + 2(0.15) + 3(0.3) + 4(0.35)

= 2.8

Var(X) = E(X²) – [E(X)]²

= 1²(0.2) + 2²(0.15) + 3²(0.3) + 4²(0.35) – (2.8)²

= 9.1 – 7.84

= 1.26