Eric Zivot
Econ 424
Winter 2016
Problem Set #2
Working with Random Variables and Probability Distributions
Suggested Solutions
Exercises
R code for solutions is in the file econ424lab2solutions.R on the class homework page.
1.
Suppose X is a normally distributed random variable with mean 0.05 and variance
(0.10)
2
.
Compute the following
•
Pr(X > 0.10)
•
Pr(X < -0.10)
•
Pr(-0.05 < X < 0.15)
•
1% quantile, q
.01
•
5% quantile, q
.05
•
95% quantile q
.95
•
99% quantile, q
.99
# X ~ N(0.05, (0.10)^2)
> mu.x = 0.05
> sigma.x = 0.10
# Pr(X > 0.10)
> 1 - pnorm(0.10, mu.x, sigma.x)
[1] 0.3085
# Pr(X < -0.10)
> pnorm(-0.10, mu.x, sigma.x)
[1] 0.06681
# Pr(-0.05 < X < 0.15)
> pnorm(0.15, mu.x, sigma.x) - pnorm(-0.05, mu.x, sigma.x)
[1] 0.6827
# q.01, q.05, q.95, q.99
> qnorm(c(0.01,0.05,0.95,0.99), mu.x, sigma.x)
[1] -0.1826 -0.1145
0.2145
0.2826
2.
Let X denote the monthly return on Microsoft Stock and let Y denote the monthly
return on Starbucks stock. Assume that X ~ N(0.05, (0.10)
2
) and Y ~ N(0.025, (0.05)
2
).
•
Using a grid of values between –0.25 and 0.35, plot the normal curves for X and
Y.
Make sure that both normal curves are on the same plot.
•
Comment on the risk-return tradeoffs for the two stocks.

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