Math 302, assignment 3
Due Oct. 1
Note: there are several questions on WebWork for this week as well. Solutions will be posted on Wed. Hand
in solutions to the questions below in class on Wed.
1. a. S
Math 302, assignment 10
Due Nov. 26
Note: there are questions on WebWork as well.
1. Assume X has variance 1, Z is a standard normal r.v. independent of X, and Y = a + bX + Z, where
b = 0.
a. Show tha
MATH 302
midterm
1. (a) Dene carefully: A probability P on a given sample space S.
(b) events A, B, C are independent.
(c) Dene carefully: The conditional probability of an event A given
an event B of
Math 302, assignment 8
Due Nov. 19
Note: there are questions on WebWork as well.
1. a.
a.
b.
c.
Let X, Y have joint density 2ex2y when x, y > 0 and 0 if either is negative. Find the density of:
X +Y.
Math 302, assignment 8
Due Nov. 12
Note: This are reworded questions posted last week. The deadline is the 12th. There are questions on
WebWork as well.
1. a. Let X1 = Geom(p1 ) and X2 = Geom(p2 ) be
Math 302, assignment 7
Due Oct. 29
Note: there are several questions on WebWork as well.
1. a. For the following random variables, compute and graph the function F (x) = P(X x).
(i) uniform on [0, 8]
Math 302, assignment 6
Due Oct. 22
Note: there are several questions on WebWork as well.
1. If X is Poi(), show that E(X n ) = E[(X + 1)n1 ]. Use this to compute E[X 2 ] and E[X 3 ].
2. a. Assuming pa
1
Math 302 Final
Instructions:
Write each answer very clearly below the corresponding question. Simplify your answer as much as possible but answers may include factorials, choose symbols or the
2
a
Math 302, assignment 4
Due Oct. 8
Note: there are several questions on WebWork for this week as well.
1. a. In a game, a player draws three cards from a deck. He wins $1 for each heart card chosen. Wh
Math 302, assignment 5
Do not hand in
Note: there are several questions on WebWork as well.
1. Let X be a Poisson random variable.
a. For a given n, nd the so that P(X = n) is maximal.
b. For a given
1
Math 302 Final - Solutions
1. (a) Carefully dene: A, B, C are independent events.
sol. For any pair, as well as for all three, the probability of the intersection is the
product of the probabilities
Midterm Solution
MATH 302
1. (a) Dene carefully: A probability P on a given sample space S.
(b) events A, B, C are independent.
(c) Dene carefully: The conditional probability of an event A given
an e