Question

Which plan has the least amount of risk? Plan A Payout P(Payout) $0 0.21 $45,000 0.53 $90,000 0.26 Plan B Payout P(Payout) −$10,000 0.26 $35,000 0.33 $75,000 0.41

Answer 1

SOLUTION:

From given data,

Which plan has the least amount of risk? Plan A Payout P(Payout) $0 0.21 $45,000 0.53 $90,000 0.26 Plan B Payout P(Payout) −$10,000 0.26 $35,000 0.33 $75,000 0.41.

Plan A

	p(x)	x*p(x)	x2 *p(x)
0	0.21	0	0
4500	0.53	2385	10732500
90000	0.26	23400	210600000000
Total	p(x) = 1	x*p(x)= 25785	x2 *p(x) =210610732500

Expected value or mean = = E(X) = x*p(x)= 25785

Variance = = V(X) = E(X² ) - [E(X)]²

Variance = = V(X) = x² *p(x) - [ x*p(x)]²

Variance = = V(X) =210610732500 - [25785​​​​​​]²

Variance = = V(X) =210610732500 - 664866225

Variance = = V(X) =209945866275

Standard deviation = = sqrt(Varience)

Standard deviation = = sqrt(209945866275)

Standard deviation = =458198.5009

Plan B

	p(x)	x*p(x)	x2 *p(x)
-10000	0.26	- 2600	26000000
3500	0.33	1155	4042500
75000	0.41	30750	2306250000
Total	p(x) = 1	x*p(x)= 29305	x2 *p(x) =2336292500

Expected value or mean = = E(X) = x*p(x)= 29305

Variance = = V(X) = E(X² ) - [E(X)]²

Variance = = V(X) = x² *p(x) - [ x*p(x)]²

Variance = = V(X) =2336292500 - [29305​​]²

Variance = = V(X) =2336292500 - 858783025

Variance = = V(X) =1477509475

Standard deviation = = sqrt(Varience)

Standard deviation = = sqrt(1477509475)

Standard deviation = =38438.3854

Hence,

From the standard deviation values of plan A and B we can say that the plan B has the lower risk.