STAT610, Fall Semester of 2013
Assignment 1
(Deadline: 9/10/2013)
1. (Ex1.8) Refer to the game of darts explained in the textbook.
(a) Derive the general formula for the probability of scoring i points.
(b) Show that P (scoring i points) is a probability
STAT610, Fall Semester of 2013
Assignment 7
(Deadline: 10/22/2013)
1. (Ex3.28) Show each of the following families is an exponential family.
(a) Gamma family with either parameter or known or both unknown.
(b) Poisson family.
2. (Ex3.34) Normal approximat
STAT610, Fall Semester of 2013
Assignment 8
(Deadline: 10/29/2013)
1. (Ex4.4) A pdf is dened by
if 0 < y < 1 and 0 < x < 2
0
f (x, y ) =
C (x + 2y )
otherwise
(a) Find the value of C .
(b) Find the marginal distribution of X .
(c) Find the joint cdf of X
STAT610, Fall Semester of 2013
Assignment 6
(Deadline: 10/15/2013)
1. (Ex3.5) A standard drug is known to be eective in 80% of the cases in which it is used. A
new drug is tested on 100 patients and found to be eective in 85 cases. Is the new drug
superio
Probability: Quiz II
June 14, 2007
Class:
No.
Name:
1. The diameter of a metal cylinder is a random variable X with a probability density function given by
fX (x) = c[1 4(x 50)2 ],
49.5 x 50.5.
c = 3.
2
(a) (4%) What is the value of c that makes fX (x) a
Chapter 4
Multiple Random Variables
4.1
Joint and Marginal Distributions
Denition 4.1.1 An n-dimensional random vector is a function
from a sample space S into Rn, n-dimensional Euclidean space.
Suppose, for example, that with each point in a sample space