Math 3338 Review for Final Exam
•Chapter 1: Only general concepts, such as, mean, median, variance,
sample, are needed. No graphing problems.
•Chapter 2: Axioms of probability, independence of events, counting
techniques (permutations, combinations). No conditional probability.
Problem 1: Events A, B are independent. P(A) = .4, P (B) = .7.
Compute P(A∩B0).
Problem 2: We select 3 distinct letters from A,B,C,D,E,F and 2 distinct
numbers from 1,2,3,4,5 to make a password.
(a) How many different passwords can we make?
(b) Find the probability that a password contains letter A.
•Chapter 3 and 4: Basic concepts such as discrete and continuous ran-
dom variables, pmf, pdf, cdf. Properties of pmf, pdf and cdf. Com-
putation of expected values, variances, moment generating functions.
Binomial distributions. Normal distributions. Transformation of ran-
dom variables.
Problem 3: Two six-sided fair dice are tossed independently. Let Xbe
the maximum of the two numbers of the tossed dice.
(a) Find the probability mass function p(x) of X.
(b) Compute the expected value of X.
Problem 4: Let MX(t) = e3t+t2and Y= 3X+ 2. Find E(Y), V (Y).
Problem 5: Let the pdf of Xbe
f(x) = (ax, 0≤x≤2;
0,otherwise.
(a) Determine the value of a.
(b) Compute P(0.5< X ≤1.5).
(c) Find cdf of X.
(d) Compute E(X) and V(X).
Problem 6: Assume that pdf of Xis f(x) = 2e−2x, x ≥0; f(x) = 0
otherwise. Find MX(t). Use MX(t) to compute E(X), V (X).
