550.311 Probability & Statistics - Fall 2012
MIDTERM 2 solutions
1. SHORT ANSWERS.
(a) Suppose X has a normal distribution with mean and variance 2 . The moment-generating function of
1 22
X is MX (t)
550.311 Probability & Statistics - FINAL EXAM SOLUTIONS
FALL 2012
1. An experiment is to independently toss a coin n times and record the number X of heads. The coin has
a probability of heads. We wis
550.311 Probability & Statistics - SPRING 2011
MIDTERM 1 SOLUTIONS
1. Suppose X and Y are jointly continuous random variables with the following joint probability density
function:
2xey if 0 < x < 1,
550.311 Probability & Statistics - SPRING 2011
NAME
MIDTERM 1
SECTION
Directions: show all work in the space provided below each problem - use the back of the page if
necessary.
1. Suppose X and Y are
550.311 Probability & Statistics - Fall 2012
NAME
MIDTERM 2
SECTION
Directions: show all work in the space provided below each problem - use the back of the page if
necessary.
1. SHORT ANSWERS.
(a) Su
550.311 Probability & Statistics - Fall 2012
MIDTERM 1 solution
1. SHORT ANSWERS.
(a) A discrete random variable X has the following probability mass function: p(x) = (.2)(.8)x1 for x =
1, 2, 3, . . .
FALL 2012
NAME mmmmmmm ....;. wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww __ SECTION ____________ __
Directions: show all work in the space provided below each problem use the back of the page if
550.311 Probability & Statistics - FALL 2011
MIDTERM 1 solution
1. Suppose X and Y are jointly continuous random variables with the following joint probability density
1
function:
2 (x + 3y ) for 0 <
550.311 Probability & Statistics - FALL 2011
NAME
MIDTERM 1
SECTION
Directions: show all work in the space provided below each problem - use the back of the page if
necessary.
1. Suppose X and Y are j
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) Comput
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