Question

The weekly demand of a​ slow-moving product has the probability mass function shown to the right.

Find the expected​ value, variance, and standard deviation of weekly demand. Type an integer or decimal, DO NOT ROUND

Demand, x	Probability, f(x)
0	0.2
1	0.3
2	0.4
3	0.1
4 or more	0.0

Answer 1

Solution:

Given that,

X	P(X)	X*P(X)	X^2*P(X)
0	0.2	0	0
1	0.3	0.3	0.3
2	0.4	0.8	1.6
3	0.1	0.3	0.9
4	0	0	0
Sum =	1	1.4	2.8

Mean :

E(X) = = X * P(X)

= 1.4

Variance :

= X² * P(X) - ()²

= 2.8 - ( 1.4 )²

= 0.84

Standard deviation:

= X² * P(X) - ()²

= Variance

= 0.84

= 0.9165