Math 3338 Exam Three Review Problems
1. Z∼N(0,12). Use table A.3 to find (a) P(Z > 1.32), (b) −0.13 ≤Z <
2, (c) 85th percentile.
2. In a city, 12% of the population do not have medical insurance. A
random sample of 40 people is selected. What is the probability that
the number of uninsured people is between 12 and 30 (inclusive).
3. Suppose Xhas a gamma distribution with parameter α, β . We know
its mean and variance are 10 and 20, respectively. Please find the values
of α, β. Use table A.4 to find P(4 ≤X≤12).
4. Suppose Xhas an exponential distribution with parameter λ. Let
Y=X3. What is fY?
5. Suppose Xhas uniform distribution on [0,1] and pdf of Yis fY(y) = 2y,
0≤y≤1; fY(y) = 0 otherwise. Is there a map gsuch that Y=g(X)?
6. X, Y are discrete random variables taking values in {0,1}. We know
some values of joint pmf p(x, y): p(0,0) = 0.3, p(1,0) = 0.1, p(1,1) =
0.34.
(a) Calculate p(0,1).
(b) Find marginal pmf pXand pY. Determine whether X, Y are de-
pendent or independent.
(c) Compute Cov(X, Y ).
7. The joint pdf of X, Y is f(x, y) = x+3
2y2, 0 ≤x≤1,0≤y≤1;
f(x, y) = 0 otherwise. Calculate E(X2Y) and ρX ,Y .
