Question

The probability distribution of a random variable X is given below. If its mean is 4.2, then the values of a and bar respectively 

X = x	1	2	3	4	5	6
P(X = x)	a	a	a	b	b	0.3

Options

• 0.3, 0.2

• 0.1, 0.4

• 0.1, 0.2

• 0.2, 0.1

Answer 1

0.1, 0.2

Explanation:

Since `sum_{x = 1}^6 P(X = x) = 1`,

a + a + a + b + b + 0.3 = 1

⇒ 3a + 2b = 0.7 ....... (i)

Mean = a + 2a + 3a + 4b + 5b + 6 (0.3)

⇒ 4.2 = 6a + 9b + 1.8

⇒ 6a + 9b = 2.4 ........(ii)

On solving (i) and (ii), we get

a = 0.1, b = 0.2