MATH 441 - MATHEMATICAL STATISTICS I
Mid Term II (Take Home Exam) Solutions
Problem 1: Find the constant K such that the following is a pdf
Kx2 , K < x < K
.
0,
otherwise
f (x) =
Solution: To be a val
Math 335-01 August 27, 2014
PROBLEM SET 2
59 4. u TAD/4.5
Instructions: Complete solutions (make your reasoning clear) for the following three
problems are due on September 3.
52
1. We know that there
Math 335-01 Nov. 14, 2014
PROBLEM SET 12 SOLUTIONS
l. The number of visits in a minute to the website for an online retail company has a Poisson distribution with
mean 20. A given visitor is a male ag
Math 335-01 November 4, 2014
PROBLEM SET 11 SOLUTIONS
1. Suppose the continuous random variable X has an exponential distribution with expected value 0.4.
Let the discrete random variable Y be deﬁned
Math 335-01 November 18, 2014
PROBLEM SET 13 SOLUTIONS
l. LetX and Y be independent random variables each having the probability density function:
x
_ _ 7
f(x)=l 2, OSxS.
0, otherwise
Calculate the pr
Math 335-01 October 27, 2014
PROBLEM SET 10
SOLUTIONS
1. Suppose the continuous random variable X has range [40,10] and probability density
function f with the property that ﬂ-x) =f(x) for all real nu
SOLUTIONS
MATH 441 HOMEWORK 1
p.12[1,9(G)], p.18[7(U),9]
p.12 #1: Suppose that A B. Show that B c Ac .
Solution:
x B c x NOT B x NOT A because A B x Ac
.
QED
p.12 #9: [Graduate] Let S be a given sampl
SOLUTIONS
MATH 441 HOMEWORK 5
p.164[2,5,8,9,10(U),12(G)]
p.164 #2: Suppose that a random variable X can have each of the seven values 3, 2, 1, 0, 1, 2, 3
with equal probability. Determine the pdf of Y
SOLUTIONS
MATH 441 HOMEWORK 2
p.34[12,15,18], p.38[10], p.44[6(U),12(G)]
p.34 #12: Suppose that 35 people are divided in a random manner into two teams in such a way
that one team contain 10 people an
SOLUTIONS
MATH 441 HOMEWORK 3
p.55[5], p.65[10,22], p.77[14,16]
p.55 #5: A box contains r red balls and b blue balls. One ball is selected at random and its
color is observed. The ball is then returne
SOLUTIONS
MATH 441 HOMEWORK 4
p.102[5], p.109[6,10], p.117[4(U),8(G),12]
p.102 #5: Suppose that a box contains seven red balls and three blue balls. If ve balls are selected at
random, without replace
MATH 441 HOMEWORK 6
Due by: Nov 5, 2008, 11 AM.
Fall 2008
1. The ow of trac at certain street corners can sometimes be modeled as a sequence of Bernoulli
trials by assuming that the probability of a c
Math 441: Mid Term III (Take Home)
Fall 2008.
Name
Solve all problems. Show all your works to receive full credit.
1. (a) If X is normally distributed with mean 2 and variance 2, express P (|X 1| 2) i
Math 441: Mid Term II (Take Home)
Fall 2008.
Due by: October 17, 2008.
Name
noindent Solve all problems. Show all your works to receive full credit.
1. Find the constant K such that the following is a
Math 441: Mid Term III
Fall 2008.
Name: Solutions
Solve all problems. Show all your works to receive full credit.
1. Solve any two of the ve parts.
(a) If X is a random variable with Poisson distribut
SOLUTIONS
MATH 441 HOMEWORK 6
#1: The ow of trac at certain street corners can sometimes be modeled as a sequence of
Bernoulli trials be assuming that the probability of a car passing during any given
MATH 441 - MATHEMATICAL STATISTICS I
Mid Term III (Take Home) Solutions Due 11.17.8
Problem 1:
(a) If X is normally distributed with mean 2 and variance 2, express P (|X 1| 2) in terms
of the standard
Math 335-01 September 24, 2014
PROBLEM SET 5
SOLUTIONS
1. Two students A and B are both registered for Math 335. Neither student has a sterling
attendance pattern. Student A attends class 75 percent o
Math 335-01 September 17, 2014
PROBLEM SET 4
SOLUTIONS
Instructions: Complete solutions (make your reasoning clear) for the following three
problems are due on Wednesday September 17.
1. Suppose on th
Math 335-01 October 14, 2014
PROBLEM SET 8 SOLUTIONS
1. Suppose thatX is a geometric random variable.
(a) Prove that for positive integers n and k, P(X =11 + k X > n): P(X = k).
w “w mm) = awe-JP mama
s
Consider the strategy where you pass the first
five offers but remember the best among the
first five, and then you select an offer in the next five
that is better than the best of the first five. I
rft
A JfunK n^v\ watksYX*
.5 and wdks t ft
relr*ln enfa*il\
S.u*h withqrchhl'!
,g . v.lhatis'lhe gvoLuibiluthat he is
wicfw_hi"' a fi
of v'b,',eh sbrhd, fllvi*
cfw_h^t hl, +akara *a( of 6o stqs.?
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Probability, solutions to Test 2
1(a) True. p(x) = P (X = x) 1 by the axioms of probability.
(b) False. Counterexample: X unif [0, 1/2] has f (x) = 2, 0 x 1/2.
(c) True. F (x) = P (X x) 1 by the axiom
Probability, Solutions to HW2
Practice problems:
31(a) There are
10
3
ways to choose the 3 numbers. To get the smallest num
ber equal to 4, the number 4 must be chosen (and there is trivially 11 =
Probability, Solutions to HW1
Practice problems:
19(a) There are 265 ways to choose 5 lowercase letters
and 102 ways to
7
choose 2 digits. For each such choice there are 2 different passwords
(choos