MIDTERM 2
NYU,Spring 2012, ProbStat
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Time: 75 min. Use of calculators is NOT permitted.
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1.
The densty function of random variable X is given by:
f (x) =
1 |x 1| for 1 |x 1| 0,
0 elsewhere.
a) Find
Section 1.2 The Basic Principle of Counting
The Basic Principle of Counting: Suppose that two experiments are to be performed.
Then if experiment 1 can result in any one of m possible outcomes and if, for each outcome
of experiment 1, there are n possible
Section 2.2 Sample Space and Events
We consider an experiment whose outcome is not predictable with certainty. However, we
suppose that the set of all possible outcomes is known.
DEFINITION: The set of all possible outcomes of an experiment is the sample
Section 4.1 Random Variables
Oftentimes, we are not interested in the specic outcome of an experiment. Instead, we are
interested in a function of the outcome.
EXAMPLE: Consider rolling a fair die twice.
S = cfw_(i, j) : i, j cfw_1, . . . , 6
Suppose we a