Question

1. A disk drive manufacturer sells storage devices with capacities of one terabyte, 500 gigabytes, and 100 gigabytes with probabilities 0.5, 0.3, and 0.2, respectively. The revenues associated with the sales in that year are estimated to be $50 million, $25 million, and $10 million, respectively.

Let X denote the estimated revenue of storage devices during that year. Determine the probability mass function of X, E(X), and Var(X).

Answer 1

let X be the random variable denote the revenue of storage devices.

$50 million revenue is associated 1 terabyte with probability ,p($50) =0.5

$25 million revenue is associated 500gigabyte with probability p($25) =0.3

$10 million revenue is associated 100gigabyte with probability p($10 =)0.2

,

so probabilty mass function will be  

X	P(X)
50	0.5
25	0.3
10	0.2

..........

X	P(X)	X*P(X)	X² * P(X)		(X-mean)² * P(X)
50	0.5	25.000	1250.000		120.125
25	0.3	7.500	187.500		27.075
10	0.2	2.000	20.000		120.050

	P(X)	X*P(X)	X² * P(X)
total sum =	1	34.5	1457.50

mean = E[X] = Σx*P(X) =            34.5000
          
E [ X² ] = ΣX² * P(X) =            1457.5000
          
variance ,var(X)= E[ X² ] - (E[ X ])² =            267.2500