Question

The probability distribution of a random variable X is given below.

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

If mean of $X$ is $4.2$, then $a$ and $b$ are respectively equal to

• A. 0.3, 0.2
• B. 0.1, 0.4
• C. 0.1, 0.2
• D. 0.2, 0.1

Answer 1

Answer: (C)

We have

x	$P(x)$	$P_i{x}_i$
1	a	a
2	a	2a
3	a	3a
4	b	4b
5	b	5b
6	0.3	1.8

$\sum P_i=a+a+a+b+b+0.3$
$\Rightarrow 1=3a+2b+0.3$
$\Rightarrow 3a+2b=0.7\dots (i)$
$\Sigma P_i{x}_i=a+2a+3a+4b+5b+1.8$
$\Rightarrow 4.2=6a+9b+1.8$
$\Rightarrow 2a+3b=0.8\dots (ii)$
Solving Eqs. (i) and (ii), we get
$a=0.1,b=0.2$