MATH 361, SPRING 2013
SHOW YOUR WORK COMPLETELY, COHERENTLY, AND LEGIBLY
There are 6 problems on this exam, each with multiple parts. Each part of each problem
is worth 4 points. '
Show your work completely to receive full
1) Suppose you choose at random a real number X from the interval [2, 10].
(a) Find the density function f(x) and the probability of an event E for this experiment,
where E is a subinterval [a, b] of [2, 10].
(b) From (a), find the probability that X > 5,
MIDTERM IN MATH 361 ON FRIDAY OCTOBER 23
There are typically 5 or 6 problems on the first midterm; each will have more than one
part. You must show your work completely to receive full credit.
SAMPLE MIDTERM I PROBLEMS, MATH 361
(1) An urn contains 20 bal
1)A fair coin is tossed 100 times. The expected number of heads is 50, and the
standard deviation for the number of heads is (100 1/2 1/2)1/2 = 5. What does
Chebyshevs Inequality tell you about the probability that the number of heads that
Simulation of Discrete Probabilities
1. As n increases, the proportion of heads gets closer to 1/2, but the difference
between the number of heads and half the number of flips tends to increase