STAT 630 Fall 2013
Homework 7 Solution
4.6.1
(a) Since X1 and X2 have the normal distributions and they are independent, thus U and
V are also normal random variables. Since E[U ] = 3 + 40 = 43, V ar(U ) = V ar(X1 ) +
52 V ar(X2 ) = 629 and E[V ] = 18 + C
630 Homework3 solution
2.4.2
(a). Since W is dened on interval [1, 4], thus P (W 5) = 0;
(b). P (W 2) =
4 2
4 1
2
= 3;
(c). P (W 2 9) = P (W 3) = 31 = 2 ;
1
4213
2 2) = P (W
2) = 41 =
(d). P (W
2 1
3.
2.4.4
In this question, we apply the fact that the i
STATISTICS 630 - Solution to Test I
October 8, 2010
1. Suppose that we toss four fair coins.
(a) Find the probability of tossing exactly one head.
Let X = the number of heads. Then P (X = 1) =
4
1
0.54 = 1/4.
(b) Find the probability of tossing an odd num
630 homework7 solution
Editor:
4.6.1
(a). Since X1 and X2 have the normal distributions and they are independent, thus
U and V are also normal random variables. Since E [U ] = 3 + 40 = 43, V ar(U ) =
V ar(X1 ) + 52 V ar(X2 ) = 629 and E [V ] = 18 + C (8)
630 homework8 solution
Editor:
6.2.4
(a). Since f (xi ; ) =
n
e xi
xi ! ,
then we can write down the log-likelihood function: l(|X ) =
n
( + xi log () log (xi !) = n + log ()
i=1
n
xi
i=1
tive with respect to and let it be zero:
l
= n +
n
log (xi !). The
630 Homework6 solution
3.5.4
First we need to obtain the marginal distribution of Y. From the joint distribution of X and Y in question
3.5.3, we can obtain: pY (2) =
2
11 , pY (3)
=
3
11 , pY (7)
=
5
11 , pY (13)
=
1
11
and pY (y ) = 0 otherwise.
(a). E
STATISTICS 630 - Solution to Test II
July 15, 2011
1. Suppose that the amount of a metal alloy produced by a factory each week is uniformly
distributed between 40 kilograms and 64 kilograms, and that the amounts produced
each week are independent. Use the
STATISTICS 630 - Solution to Test I
June 21, 2011
1. Let A be the event that your right knee is sore on a given morning and B be the event
that your left knee is sore on that morning. Suppose that P (A) = 0.4 and P (B ) = 0.5.
What the probability that at
STATISTICS 630 - Solution to Final Exam
December 14, 2010
1. Suppose that the time (in minutes) that a professor takes to grade a single nal exam is a
uniform random variable on the interval [6, 12]. Suppose that the professor has to grade
48 nal examinat