Question 1
The students in a course will form study groups. There are a total of 12 students in
the class and a study group consists of 3 students selected at random.
(a) ( 5 points) How many different study groups are possible?
(b) cfw_ 5 points) If the

10.3.1 Let W be an exponential random variable with PDF
WWW
%
waO.
otherwise.
fw (w) = l 3"
Find the CDF FXQ) (x) of the time delayed ramp
process X (t) = t W.
10.8.1 X n is an iid random sequence with mean E[Xn]=
z p, X and variance Var[X,]_ (TX. What 15

4.1.3 For continuous random variables X, Y with joint
% CDF Fx,y(x, y) and marginal CDFs FX(x) and
Fy(y),ndP[x1 5 X < x2 Uyl 5 Y < yz]. This
is the probability of the shaded cross region in the
following diagram.
Y
4.4.1 Random variables X and Y have th

4.9.3 X and Y have joint PDF
a
(4x +2y)/3 0 5 x 51;
fx,y(x.y)= OSysl,
0 otherwise.
(a) For which values of y is fxly(x|y) dened?
Whatis fX|y(x|y)?
(b)For which values of x is fyXQIIx) dened?
What is fy|X(ylx)?
4.9.11 Random variables X and Y have joint PD