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. Suppose events A, B, C are independent, and have probabi
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 that (X, Y ) = b2b+2 .
b. Find lim (X, Y ) and lim0 (X, Y
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 positive probability.
(d) State the law of total proba
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.
min(X, Y ).
max(X, Y ).
2. X, Y are a uniform point in
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 independent Geometric random variables. What is the
dis
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]
(ii) Exp(4)
1
(iii) Bin(5, 2 ).
b. In each of these cas
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 pairs of individuals are approximately independent, estim
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
exponential function. You may also use the function (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. What is
the expected amount won?
b. If additionally the p
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 , nd the n so that P(X = n) is maximal.
2. Assume each
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.
(b) Suppose that X, Y and Z are independent random va
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 event B of positive probability.
a. P is a function from