Random Variables – Examples
1. Let
X
be the number of televisions in an apartment, to be randomly selected in a small
town. Suppose that
X
has probability mass function:
x
0
1
2
p
(
x
)
0.2
0.7
0.1
(a) Compute the mean/expected value of
X
.
(b) What is the probability that this apartment will have at most 2 televisions?
(c) What is the probability that this apartment will have either exactly 0 televisions
or exactly 2 televisions?
2. Let
X
be the amount of time (in minutes) it will take to complete and handin an
exam (where the exam must be handedin no later than 50 minutes from the start).
Suppose that
X
has a probability density function (pdf):
f
(
x
) =
1
20
if 30
≤
x <
50
0
otherwise
(a) Compute the probability this exam will be handedin before 20 minutes have
passed.
(b) Compute the probability this exam will be handedin when exactly 30 minutes
have passed.
(c) Compute the probability this exam will be handed in before 32 minutes have
passed.
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 Spring '08
 Staff
 Probability, Probability theory, probability density function, randomly selected item

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