1) Suppose that X is a finite random variable that can assume only the values 1, 5, 10,
and 20. The values of the p.m.f., f X , are given by f X (1)  0.50 , f X (5)  0.30 ,
f X (10)  0.15 , and f X (20)  0.05 . Compute the expected value of X.
2) Let X be the random variable whose c.d.f. is given below.
0.0
0.2

FX ( x)  0.5
0.7

1.0
if
if
if
if
if
x2
2 x4
4 x6
6 x8
8 x
Compute the mean, μ X . Hint: First identify all possible values of X , then compute
values for the p.m.f., f X (x) .
3) Let X be an exponential random variable with parameter   0.5 . (i) Use FX to
compute P(0.2  X  1.2) . (ii) Use f X to compute the same probability.
4) Let X be a continuous random variable whose p.d.f. is give by
1.5  x  0.75  x 2
f X ( x)  
0
if 0  x  2
elsewhere
.
Compute the expected value of X.
5) Let X be an exponential random variable with  X  3.5 . Compute the following. (i)
f X (2) . (ii) P( X  2) . (iii) FX (2) . (iv) P( X  2) . (v) E ( X ) .
6)
Let X be a random variable whose p.m.f. is given below.
x
f X (x)
compute V ( X ) and  X .
1
0.2
0
0.4
1
0.2
2
0.1
4
0.1
7)
Let X be a binomial random variable with n  6 and p  0.3 . Use the special formulas
for mean and variance that apply only to binomial random variables, to compute the
mean, variance, and standard deviation of X.
8)
Let X be the continuous uniform random variable on [0,10] . Compute the mean, variance,
and standard deviation of X.
9)
Let X be a random variable with a mean of 75 and a standard deviation of 6. Let x be
the sample mean for random samples of size n  20 . Compute the expected value,
variance, and standard deviation of x .