Lecture 10 Class Notes
The GoferBroke company owns a tract of land that may contain oil.
A consulting geologist has reported to management that she believes there is a 1 chance
in 4 of oil.
Because of this prospect, another oil company has offered to p

Lecture 9 Notes
Poisson distribution
This is a counting distribution.
The random variable of interest is concerned with the number of outcomes that occur
during some interval of time or on some area.
Parameter of Poisson distribution is l = the rate pe

Lecture 8 Notes
There is an urn that consists of 4 black and 2 green balls. The experiment is defined such
that a ball is selected from the urn and then returned (i.e. with replacement). We repeat
this experiment three times and are interested in the num

Lecture 7 Notes
Cumulative
Distribution
Discrete
F(x) CDF is defined for every number
x by
F ( x) = P( X x ) = f (t )
Continuous
F(x) CDF is defined for every
number x by
F ( x) = P ( X x ) =
P( a X b)
x
t x
f (t )dt
It is the probability that the obser

Lecture 6 Notes
Find PMF of X:
Step 1. We know the upper and lower bound of the distribution just from looking at the
CDF. The possible values of X are 0,1,2,3 and 4.
Step 2. For each possible value, calculate the P(X=x).
A continuous random variable has

Lecture 5 Notes
Properties of Distributions:
1. The probability of random variable X taking on a value x (or set of values) is positive.
We can never have a negative probability
2. Calculating the probability over the entire set of values is equal to 1.

Lecture 4 Notes
Discrete Sample Space: If a sample space contains a finite number of possibilities or an
unending sequence with as many elements as there are whole numbers, it is called a
discrete sample space.
Example: Coins in the Jar Experiment from

Lecture 3 Notes
In Class Problem:
A customer has approached a bank for a loan. Without further information, the bank
believes there is a 4% chance that the customer will default on the loan. The bank can
run a credit check on the customer.
The check wil

Lecture 2 Class Notes
Example:
Suppose we have a fuse box, containing 20 fuses, of which 5 are defective. If 2 fuses are
selected at random and removed from the box in succession without replacing the first,
what is the probability that both fuses are de

Lecture 1 Notes
Experiment: a process by which an observation is obtained. For example, roll of a die,
toss of a coin.
Sample Space: The set of all possible outcomes of an experiment. For example:
Event: a collection of outcomes in the sample space.
F