Question

A multinational company invests a certain amount of dollars in a project. The following table lists all the possible future returns ($, in millions) associated with the respective probabilities.

Let X represent the returns ($, in millions) in this random process. Calculate the population variance σ 2 of X ($, in squared millions). (keep two decimals).

	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Scenario 6	Scenario 7
Possible returns, Xi	14.33	-8.98	14.77	-12.18	10.27	-8.95	-9.39
Probability, pi	15.25%	7.50%	13.55%	16.75%	10.50%	18.05%	18.40%

Group of answer choices

72.81

229.27

433.97

132.90

Answer 1

Solution :

x	P(x)	x * P(x)	x2 * P(x)
14.33	0.1525	2.185325	31.31571
-8.98	0.075	-0.6735	6.04803
14.77	0.1355	2.001335	29.55972
-12.18	0.1675	-2.04015	24.84903
10.27	0.105	1.07835	11.07465
-8.95	0.1805	-1.61548	14.4585
-9.39	0.184	-1.72776	16.22367
Sum	1	-0.79188	133.5293

Variance = ²

= X ² * P(X) - ²

= 133.5293 - (-0.79188)²

= 132.90