*EECS 126 Fall 2001
Midterm 1
The exam starts at 3:40 p.m. sharp and ends at 5:00 p.m. sharp.
There are 5 problems. The maximum score is 50 points.
The exam is open book open notes.
Problem #1
For each of the following statements, indicate whether you believe that the statement is
true or believe it is false, and give a briefs explanation of your reasoning. A correct answer
without a valid explanation gets 1 points. A correct answer with a valid explanation gets 3 points.
(a) For any three events A, B, and C, if P (A B) > 0 and P(B C) > 0,
then P (A C) > 0.
(b) Given two events A and B with P(A) > 0 and P(B) > 0 , if P( A | B) > P(A) then
P(B|A) > P(B).
(c) Two card are drawn at random without replacement from as standard deck of 52
playing cards
(i.e. the first card is drawn at random and then the second card is drawn at random from
the remaining cards.)
Then the event that the two cards are both aces is independent of the event that they are
both diamonds.
(d) g(x) is a real valued function on R satisfying g(x) >= x. Let X be a random variable
and let Y = g(X).
The FY(z) <= FX(z) for all z R.
(e) Adding a constant to a random variable does not change its standard deviation.
(f) A random variable X is known to satisfy FX(-2) = 0 and FX(10) = 1. Then it must
have finite variance.
(g) If X is a random variable and Y = X 1/3, then the characteristic function of Y can be
determined from
the characteristic function of X.
EECS126, exam #1, Fall/2001
EECS12, Fall/2001exam #1professor Unknown 1
