Suppose we throw three identical, fair six-sided dice. The six sides of each die are
labeled 1, 2, 3, 4, 5, and 6.
What is the probability that the three numbers of the three dice are all
different? (5%)
Suppose we throw three identical, fair six-sided dice. The six sides of each die are
labeled 1, 2, 3, 4, 5, and 6.
How many possibilities are there for the set of numbers appearing on the
three dice? (For example, if all three dice show 2, this set is {2}. If the
numbers are 5, 2, and 3, this set is {2, 3, 5}.) (5%)
Suppose a permutation of all 26 lowercase letters is selected at random with each
permutation equally likely.
What is the probability that the first 13 letters of the permutation are in
order? (5%)
Suppose a permutation of all 26 lowercase letters is selected at random with each
permutation equally likely.
What is the probability that a and b are not next to each other? (5%)
Given a 6-sided die for which each of the values 1 through 6 comes up with
equal probability, what is the conditional probability of rolling a 6 given
that the last 3 times you rolled you also got a 6? (10%)
What is the expected value of a roll of one 6-sided die assuming each of the
values 1 through 6 comes up with equal probability? (10%)
Suppose that a random variable X follows the distribution given by:
What is the value of P(X2 > 1) ? (5%)
Suppose that a random variable X follows the distribution given by:
Suppose that a value of X has occurred and that the value is an even
number. What is the probability that the value of X is 0? (5%)
Suppose that a random variable X follows the distribution given by:
Suppose that a sample of 2 is taken from the distribution obtaining X1
and X2 . What is Var[X1 + 2X2 ] ? (10%)
Suppose that X ~Binomial(10, 0.5) and statistically independent of Y ~
Binomial(20, 0.5). What is W = X +Y distributed? (10%)
A researcher chooses a sample of size n = 100 from a population in such a
way that every set of n units from that population has an equal
probability of being the sample actually selected. This is a (10%)
stratified random sample.
systematic random sample.
simple random sample.
non-random sample.
The least-squares regression line is (10%)
The line that makes the square of the correlation in the data as large as
possible.
The line that makes the sum of the squares of the vertical distances of
the data points from the line as small as possible.
The line which best splits the data in half, with half of the points above
the line and half below the line.
All of the above.
20% of M&M chocolates are blue. What is the probability that between
17% and 22% of a random batch of 400 M&M chocolates are blue? (10%)
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