Question

The probability distribution of the random variable X is given by

X = x	0	1	3	7
P(X = x)	0.3	0.4	0.1	0.2

Then, 4 var (X) - E (X²) is equal to ______ 

Options

• 2.24

• 19.2

• 15.66

• 14.96

Answer 1

The probability distribution of the random variable X is given by

X = x	0	1	3	7
P(X = x)	0.3	0.4	0.1	0.2

Then, 4 var (X) - E (X²) is equal to 15.66.

Explanation:

E(X) = ∑x_i . p(x_i) = 2.1

`E(X^2) = sumx_i^2 . P(x_i) = 11.1`

Var(X) = `E(X^2) - [E(X)]^2`

= 11.1 - 4.41

= 6.69

Now, 4 var(X) - E(X²) = 4(6.69) - 11.1

= 26.76 - 11.1

= 15.66