Question

You are examining two stock options of equal cost. Stock for Green Industries rises 6% of the time by $3, 7% of the time drops by $2, otherwise has no change. Stock for Purple Corp. loses $5 4% of the time, gains $3 8% of the time, otherwise has no change. Calculate the expected value, variance, and standard deviation. Last decide which is the better stock to invest in using the data you calculated and explain your choice.

Answer 1

for  Green Industries:

x	f(x)	xP(x)	x2P(x)
3	0.06	0.180	0.540
-2	0.07	-0.140	0.280
0	0.87	0.000	0.000
	total	0.040	0.820
	E(x) =μ=	ΣxP(x) =	0.0400
	E(x2) =	Σx2P(x) =	0.8200
	Var(x)=σ2 =	E(x2)-(E(x))2=	0.8184
	std deviation=	σ= √σ2 =	0.9047

expected value =0.04

variance =0.8184

and std deviaiton =0.9047

for  Purple Corp.:

x	f(x)	xP(x)	x2P(x)
-5	0.04	-0.200	1.000
3	0.08	0.240	0.720
0	0.88	0.000	0.000
	total	0.040	1.720
	E(x) =μ=	ΣxP(x) =	0.0400
	E(x2) =	Σx2P(x) =	1.7200
	Var(x)=σ2 =	E(x2)-(E(x))2=	1.7184
	std deviation=	σ= √σ2 =	1.3109

expected value =0.04

variance =1.7184

and std deviaiton =1.3109

here as expected value is same for both of stocks but standar ddeviaiton of Green Industries is small

therefore one must invest in Green Industries