ECE331 HOMEWORK 5

(0)[reading corresponding with the lectures] 
Read Yates chapter 4

(1) Yates 4.1.3. Also find the pdf of U

(2) Yates 4.3.1

(3) Quiz 4.5

(4) Yates 4.5.4. Let C be the same peak temperature 
in Antartica but measured in degrees Celsius.
What is the mean and standard deviation of C?

(5) Yates 4.5.7

(6) Yates 4.6.4

(7) Yates 4.6.6

(8) Suppose X is uniformly distributed over 
[-2,1] and Y=X^2 ("X squared").
Find the CDF of Y and then the PDF of Y.

(9) Quiz 4.3

(10) Quiz 4.8

(11) Yates 4.7.14

(12) (a) Yates 4.7.16. It follows from the answer to 4.7.16
that the PDF of X is f(x).
(b) Compute the CDF F and the inverse of F for 
an exponential random variable with parameter a=2.
(c) Write a computer program that uses a uniform 
random variable generator and the results from (a) and (b) to 
generate 10000 samples of an exponential random 
variable with parameter a=2.
(d) Do further programming to accomplish the following:
Count the number of samples in part (c) in each of 30 bins of 
size 0.1 in a range from 0 to 3.
Use the counts to compute a discrete approximation to the 
pdf of an exponential random variable with one value 
corresponding to each bin.
(e) Check the answer to (d) by plotting the discrete 
approximation in (c) on the same plot as the exact PDF of 
a continuous exponential random variable with parameter a=2.

(13) Let X and Y be discrete random variables.
(a) Prove that E[X+Y]=E[X]+E[Y].
(b) Prove that if X and Y are independent, then E[XY]=E[X]E[Y].
(c) Give an example of X and Y NOT independent and E[XY] = E[X]E[Y]
FALSE.