PROBABILITY AND STATISTICS FOR THE BIOLOGICAL SCIENCES AND ENGINEERING
MATH 550.310

Summer 2012
Homework Problems in Probability
Collected for 550.310 and 550.311; many are taken from textbooks by Jay Devore, Neil Weiss,
Bernard Rosner, John Rice, Sheldon Ross, Cincich, Levine & Stephan, Walpole, Myers, Myers,
& Ye.
1
Probability basics
1.1
(Devore
PROBABILITY AND STATISTICS FOR THE BIOLOGICAL SCIENCES AND ENGINEERING
MATH 550.310

Summer 2012
Homework Problems
Random Variables
Collected for 550.310; many are taken from textbooks by Jay Devore, Neil Weiss, Bernard Rosner,
John Rice, Sheldon Ross, Cincich, Levine & Stephan, Walpole, Myers, Myers, & Ye.
1
Discrete Random Variables
1.1
Two fair si
PROBABILITY AND STATISTICS FOR THE BIOLOGICAL SCIENCES AND ENGINEERING
MATH 550.310

Spring 2014
550.310 Probability & Statistics  SPRING 2013
MIDTERM 1 SOLUTION
1. Suppose X and Y are random variables that have the following joint distribution:
x y if 1 x 2, 0 y 1
f (x, y) =
0
if otherwise.
(a) Determine the marginal distribution of X. If 1 x 2, th
PROBABILITY AND STATISTICS FOR THE BIOLOGICAL SCIENCES AND ENGINEERING
MATH 550.310

Spring 2014
550.310 Probability & Statistics  Spring 2013
MIDTERM 2 solutions
cfw_
1. Let X and Y be jointly continuous rvs having joint p.d.f. f (x, y) =
x + y for 0 < x < 1, 0 < y < 1
.
0
otherwise
(a) Compute E(XY ).
cfw_
11
11 2
x3 y
2 ) dx dy = 1
E(XY ) = 0 0 x
Probability and Statistics Review Sheet
Drew Bobesink
Probability A number between zero and one measuring the likelihood of an outcome occurring Frequentist Approach Repeating an experiment ad infinitum gives probability Bayesian Approach Probability is a
Prob/Stat Review Midterm 2
Expected Value
The expected value, or mean, , or E(x), of a function can be defined as a weighted average of values, or as the fair market value of a function's output For a discrete r.v. with probability p, the expected value
PROBABILITY AND STATISTICS FOR THE BIOLOGICAL SCIENCES AND ENGINEERING
MATH 550.310

Spring 2014
1. (a) Use the tables provided to nd P (1.32 Z 2.44) and P (Z > 1.88), where Z is a standard normal
random variable. Clearly label each calculation.
P (1.32 Z 2.44) = P (Z 2.44) P (Z < 1.32) = .9927 .9066 = .0861 and P (Z > 1.88) = 1 P (Z
1.88) = 1 .9699