Introduction to Probability
Math 30530, Section 01 Fall 2012
Homework 9 Solutions
1. During a season, a basketball team plays 70 home games and 60 away games. The
coach estimates at the beginning of t
Introduction to Probability
Math 30530, Section 01 Fall 2012
Homework 6 Solutions
1. GW 17.2
Solution: a) 0, 1, 2, 3, . . . Its Poisson because were counting number of occurrences of an event, with di
Introduction to Probability
Math 30530, Section 01 Fall 2012
Homework 2 Solutions
1. For events A and B with Pr(A) > 0, Pr(B) > 0, we say that A is positively correlated
with B if Pr(A|B) > Pr(A) (in
Introduction to Probability
Math 30530, Section 01 Fall 2012
Homework 4 Solutions
1. GW 8.2
Solution: For x 1, y 1 (and integers),
Pr(X = x, Y = y) = (.99)x1 (.01)(.97)y1 (.03)
(here using independenc
Introduction to Probability
Math 30530, Section 01 Fall 2012
Homework 1 Solutions
1. A box contains four candy bars: two Mars bars, a Snickers and a Kit-Kat. I randomly
draw a bar from the box and eat
Introduction to Probability
Math 30530, Section 01 Fall 2012
Homework 3 Solutions
1. You are in a room with ve doors, and your host tells you that behind two randomly
chosen doors he has placed a priz
I CDMWWWO=UWBNJLM®M=Wmf+NWpnzwm
py(0) = 5/25, and p(l, O) = 1/25. Since [20, 0) aé px(l)py(0), X and Y are dependent.
Magma?er
By the independence of X and Y, ' ~r .
P(X = 1, Y = 3) = P(X =1)P(Y = 3
Introduction to Probability
Math 30530, Section 01 Fall 2012
Homework 5 Solutions
1. GW 15.7
a) If X is number of draws, then X Geometric(4/52), so E(X) = 52/4 = 13.
b) Taking at least four is the sam
Introduction to Probability
Math 30530, Section 01 Fall 2012
Homework 8 Solutions
1. GW 29.1a): The joint density is 2/9 on the triangle (and 0 elsewhere).
E(X + Y ) =
triangle
2. GW 29.4:
2
(x + y) d
Hangover/5K (C5 chalx'ms
@ Let f be the probability density function of a gamma random variable with parameters r and
A. Then XXVI?
f (x) '- "56?"
Therefore,
I A, r - x r-2 _, Ar+l r2 M . r 1
f
Introduction to Probability
Math 30530, Section 01 Fall 2012
Homework 7 Solutions
1. GW 25.1: The area of the triangle is 9/2, so on the triangle the joint density is
2/9; everywhere else it is 0. The