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BME 423
HOMEWORK #1
Fall 2006
1. Suppose that a random variable (RV) X can take on only the values 2, 0, 1, and 4, and that
the probabilities of these values are as follows: Pr(X = 2) = 0.4, Pr(X = 0) = 0.1, Pr(X = 1) =
0.3, and Pr(X = 4) = 0.2.
Sketch the d.f. of X.
2. Suppose the d.f. of a RV X is as follows:
(
29
2
0
0
1
0
3,
9
3.
1
x
F x
x
x
x
F
F
F
F
=
<
Find & sketch the p.d.f.
of
X.
3. In a class of 50 students, the number of students n
i
of each age i is shown in the following
table:
Age i
n
i
18
20
19
22
20
4
21
3
25
1
What is the expected value of the age of a student randomly selected form this class?
4. Suppose that X has a uniform distribution on the interval [0, 2].
Compute the variance of X.
5. Suppose that X has a normal distribution for which the mean is 1 and the variance is 4.
Find
the value of each of the following probabilities:
a. Pr(X ≤ 3);
b. Pr(X
> 1.5);
c. Pr(2 < X < 5);
d. Pr(1 < X < 0.5).
6. Suppose that X has a normal distribution for which the mean is 1 and the variance is 4. Find
the value of x that satisfies the each of the following relationships: a. Pr(X < x) = 0.1 (10
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 Fall '06
 D'Argenio
 Biomedical Engineering

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