STAT 36-217, HW4, due Tuesday 10/11/2011, 11:50 AM
This HW is slightly harder than usual as you have about 2 weeks to complete. Start
earlier when possible and seek help during oce hours if you have p
36-217, Fall 2013
Homework 6 Solutions
1. (15 points)
a. Note that, after one week the expected price of the commodity is 1/2 + 4 1/2 = 5/2 dollars per ounce.
Since, 5/2 > 2, if I want to maximize the
36-217, Fall 2013
Homework 5 Solutions
1.
a. (5 points)
P (A|B C) =
(A and B are conditionally independent) =
P (A B|C)P (C)
P (B C)
P (A|C)P (B|C)
P (A|C)P (B|C)P (C)
=
= P (A|C)
P (B C)
P (B|C)
b. (
36-217, Fall 2013
Homework 3 Solutions
1. (15 points) Consider an event A , and dene A B = C. Note that: B and A , C .
By Bayes rule, we can write:
P (A|B) =
P (A B)
P (C)
=
.
P (B)
P (B)
Since, P (.)
36-217, Fall 2013
Homework 4 Solutions
1. (20 Points) Let Ai denote the event that all the points lie in the semicircle beginning at the ith points and
going clockwise for 180deg, i = 1 . . . n. A is
36-217, FALL 2013
Homework 1 Solutions
1.
a. (3 points) If we arbitrarily choose some element x from a non-empty set (A B c ), then x is
either in A or not B. Thus, x should be in A. This implies (A B
36-217, Fall 2013
Homework 7 Solutions
1. (15 points)
a. First, lets show that E(X) = np.
n
E(X) =
xi P (X = xi ) where xi = 0, . . . , n
i=0
n
=
n xi
p (1 p)nxi
xi
xi
i=0
n
=
np
i=0
(n 1)!
pxi 1 (1 p
36-217, Fall 2013
Homework 10 Solutions
1. (a.) [2 points] Since Y unif orm(a, b), cdf of Y is:
0 if x < a
FX (x) = xa if a x < b
ba
1 if x b
(b.) [5 points]
FX (x) = P (X x) = P (X x|Z = 1)P (Z = 1)
36-217, Fall 2013
Homework 8 Solutions
1. (25 points) Bubble sort algortihm again
Using the fact that the expected value of a sum of random variables is equal to the sum of the expectations,
we see th
36-217, Fall 2013
Homework 2 Solutions
1. (12 points) The information given by the problem can be organized in a Venn diagram as presented in Figure
1. Firstly, note that in the triple intersection of