The probability distribution of a random variable X is given below. x = k 0 1 2 3 4 P(X = k) 0.1 0.4 0.3 0.2 0 The variance of X is

Question

The probability distribution of a random variable X is given below. x = k 0 1 2 3 4 P(X = k) 0.1 0.4 0.3 0.2 0 The variance of X is (A) 1.6 (B) 0.24 (C) 0.84 (D) 0.75

Tardigrade Admin · Accepted Answer

We have, X P(X) Pi Xi PiX2i 0 0.1 0 0 1 0.4 0.4 0.4 2 0.3 0.6 1.2 3 0.2 0.6 1.8 4 0 0 0 Sigma Pi Xi=1.6 Sigma Pi Xi2=3.4 Variance (σ2) = Sigma Pi Xi2-( Sigma Pi Xi)2 =3.4-(1.6)2=3.4-2.56=0.84

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

x = k 0 1 2 3 4

P(X = k) 0.1 0.4 0.3 0.2 0

The variance of X is

1.6

0.24

0.84

0.75

We have,

$X$ $P (X)$ $P_{i} X_{i}$ $P_{i} X_{i}^{2}$

0 0.1 0 0

1 0.4 0.4 0.4

2 0.3 0.6 1.2

3 0.2 0.6 1.8

4 0 0 0

$Σ P_{i} X_{i} = 1.6$ $Σ P_{i} X_{i}^{2} = 3.4$

Variance $(σ^{2}) = Σ P_{i} X_{i}^{2} - (Σ P_{i} X_{i})^{2}$
$= 3.4 - (1.6)^{2} = 3.4 - 2.56 = 0.84$

$X$	$P (X)$	$P_{i} X_{i}$	$P_{i} X_{i}^{2}$
0	0.1	0	0
1	0.4	0.4	0.4
2	0.3	0.6	1.2
3	0.2	0.6	1.8
4	0	0	0
		$Σ P_{i} X_{i} = 1.6$	$Σ P_{i} X_{i}^{2} = 3.4$

Q. The probability distribution of a random variable X is given below. x = k 0 1 2 3 4 P(X = k) 0.1 0.4 0.3 0.2 0 The variance of X is

1.6

0.24

0.84

0.75

We have, X P(X) Pi​Xi​ Pi​Xi2​ 0 0.1 0 0 1 0.4 0.4 0.4 2 0.3 0.6 1.2 3 0.2 0.6 1.8 4 0 0 0 ΣPi​Xi​=1.6 ΣPi​Xi2​=3.4 Variance (σ2)=ΣPi​Xi2​−(ΣPi​Xi​)2 =3.4−(1.6)2=3.4−2.56=0.84

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

x = k 0 1 2 3 4

P(X = k) 0.1 0.4 0.3 0.2 0

The variance of X is

We have,

$X$ $P (X)$ $P_{i} X_{i}$ $P_{i} X_{i}^{2}$

0 0.1 0 0

1 0.4 0.4 0.4

2 0.3 0.6 1.2

3 0.2 0.6 1.8

4 0 0 0

$Σ P_{i} X_{i} = 1.6$ $Σ P_{i} X_{i}^{2} = 3.4$

Variance $(σ^{2}) = Σ P_{i} X_{i}^{2} - (Σ P_{i} X_{i})^{2}$
$= 3.4 - (1.6)^{2} = 3.4 - 2.56 = 0.84$