is the measure of ones belief that a future (random)
event will occur.
event is one whose occurrence cannot be predicted
However, we can often understand the long-run :
Chapter 3. Discrete random variables and probability
variable (r.v.) is a function that takes a sample point
in S and maps it to it a real number.
That is, a r.v. Y maps the sample space (its domain) to the real
Chapter 6: Functions of Random Variables
We are often interested in a function of one or several random
variables, U(Y1 , . . . , Yn ).
We will study three methods for determining the distribution of a
function of a random variable:
1. The method of cdfs
In many applications we measure several r.v.s per individual.
For a set of households, we can measure both income and the
number of children.
For a set of giraffes, we can measure their height and weight.
We can m
Continuous random variables
Continuous r.v.s take an uncountably infinite number of possible
Heights of people
Weights of apples
Diameters of bolts
Life lengths of light-bulbs
We cannot assign positive probabilities to every partic
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Question Points Score
1. (8 points) (Monty Hall, Aga
Test 2 Solutions
1. Let the random variable Y have distribution function
F (y) = y2
0 < y < 2,
2 y < 4,
(a) (5 points) What is the probability density function of
in the denition of F !)
Solution. This is ex