Learning Materials
Features
Discover
Chapter 4: Q13E (page 234)
Let X have the binomial distribution with parameters5 and 0.3. Find the IQR of X. Hint: Return to Example3.3.9 and Table 3.1.
The IQR of X is 1.
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Suppose thatXis a random variable for which the m.g.f. is as follows:\(\psi \left( t \right) = \frac{1}{5}{e^t} + \frac{2}{5}{e^{4t}} + \frac{2}{5}{e^{8t}}\)for鈭掆垶< t <鈭�.Find the probability distribution ofX. Hint:It is a simple discrete distribution.
Let X have the Cauchy distribution (see Example4.1.8). Prove that the m.g.f. \(\psi \left( t \right)\) is finite only for\(t = 0\).
Consider the conditions of Exercise 7 again. If the value of Y is to be predicted from the value of X, what will be the minimum value of the overall M.S.E.?
Suppose that a point is chosen at random on a stick of unit length and that the stick is broken into two pieces at that point. Find the expected value of the size of the longer piece.
Consider the situation of pricing a stock option as in
Example 4.1.14.We want to prove that a price other than \(20.19 for the option to buy one share in one year for \)200 would be unfair in some way.
a.Suppose that an investor (who has several shares of
the stock already) makes the following transactions.
She buys three more shares of the stock at \(200 per
share and sells four options for \)20.19 each. The investor
must borrow the extra \(519.24 necessary to
make these transactions at 4% for the year. At the
end of the year, our investor might have to sell four
shares for \)200 each to the person who bought the
options. In any event, she sells enough stock to pay
back the amount borrowed plus the 4 percent interest.
Prove that the investor has the same net worth
(within rounding error) at the end of the year as she
would have had without making these transactions,
no matter what happens to the stock price. (Acombination
of stocks and options that produces no change
in net worth is called a risk-free portfolio.)
b.Consider the same transactions as in part (a), but
this time suppose that the option price is \(xwhere
x <20.19. Prove that our investor loses|4.16x鈭�84触
dollars of net worth no matter what happens to the
stock price.
c.Consider the same transactions as in part (a), but
this time suppose that the option price is \)xwhere
x >20.19. Prove that our investor gains 4.16x鈭�84
dollars of net worth no matter what happens to the
stock price.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine