Question

6. -/3 points v My Notes You are trying to decide whether or not to book a cheap flight to fly home from NCSU after your final exams, but you're not sure when your last exam will be. You think there is a 25% chance that your last exam will be scheduled after the last day that you can get a seat on the cheap flight. If it turns out that your last exam is scheduled after the last day that you can get a seat on the cheap flight, then you will have to cancel the flight, resulting in a loss to you of $150. If you can take the cheap flight home you will save $100. Question 1. If you book the cheap flight, what is your expected gain? dollars Question 2. If you book the cheap flight, what is the standard deviation of your gain? (Use 2 decimal places in your answer.) dollars

Answer 1

from above:

below is pmf of X (net gain):

x	f(x)	xP(x)	x2P(x)
100	0.7500	75.00000	7500.00000
-150	0.2500	-37.50000	5625.00000
total		37.5000	13125.0000
	E(x) =μ=	ΣxP(x) =	37.5000
	E(x2) =	Σx2P(x) =	13125.0000
	Var(x)=σ2 =	E(x2)-(E(x))2=	11718.7500
	std deviation=	σ= √σ2 =	108.2532

1)expected gain =37.5

2) standard deviation =108.25