For the probability distribution given by X=xi 0 1 2 pi (25/36) (5/18) (1/36) the standard deviation (σ) is

Question

For the probability distribution given by X=xi 0 1 2 pi (25/36) (5/18) (1/36) the standard deviation (σ) is (A) √(1/3) (B) (1/3) √(5/2) (C) √(5/36) (D) None of the above

Tardigrade Admin · Accepted Answer

Variance =∑ xi 2pi -(∑ xi pi)2 = [0+ (5/18) + (1/9)] - [0+ (5/18) + (2/36)]2 = (14/36)- (1/9) = (10/36) = (5/18) Standard deviation, σ = √(5/18) = (1/3) √(5/2)

$X = x_{i}$	0	1	2
$p_{i}$	$\frac{25}{36}$	$\frac{5}{18}$	$\frac{1}{36}$

Q. For the probability distribution given by

$X = x_{i}$ 0 1 2

$p_{i}$ $\frac{25}{36}$ $\frac{5}{18}$ $\frac{1}{36}$

the standard deviation $(σ)$ is

$\frac{1}{3}$

$\frac{1}{3} \frac{5}{2}$

$\frac{5}{36}$

None of the above

Variance $= \sum x_{i}^{2} p_{i} - (\sum x_{i} p_{i})^{2}$
$= [0 + \frac{5}{18} + \frac{1}{9}] - [0 + \frac{5}{18} + \frac{2}{36}]^{2} = \frac{14}{36} - \frac{1}{9} = \frac{10}{36} = \frac{5}{18}$
Standard deviation, $σ = \frac{5}{18} = \frac{1}{3} \frac{5}{2}$

Q. For the probability distribution given by X=xi​ 0 1 2 pi​ 3625​ 185​ 361​ the standard deviation (σ) is

31​​

31​25​​

365​​