Question

This is how many classes students at Bronx College take this semester with the probabilities

courses	1	2	3	4	5
probability (distribution) of taking that many courses	.1	.1	.6	.1	.1

The variance for this distribution is approximately

Answer 1

The probability distribution is,

Courses ( X )	Probability ( P(X) )	X * P(X)	X2 * P(X)
1	0.1	0.1	0.1
2	0.1	0.2	0.4
3	0.6	1.8	5.4
4	0.1	0.4	1.6
5	0.1	0.5	2.5
		$\sum X * P(X) = 3$	$\sum X^2 * P(X) = 10$

The expected value of X is,

$E(X)= \sum X* P(X) = 3$

The variance of X is,

$Var(X)= \sum X^2* P(X) - [ E(X)]^2 = 10 - [ 3]^2 = 10-9 = 1$

The variance for given distribution is approximately 1