Probability Theory Flashcards
Define sample space
The set S of all possible outcomes of a random experiment is called the sample
space for the experiment
Define event
An event is any collection of possible outcomes of an experiment, that is, any
subset of A ⊆ S.
How do you find the power set of a set of sets? - set of all subsets
The total number of subsets for a set of ‘n’ elements is given by 2^n
What does pairwise disjoint mean
Intersections are zero and their sum is the whole sample space
When does the law of total probability apply
When a partition is formed
Define independent events
Two events A and B are said statistically independent iff
P(A ∩ B) = P(A)P(B)
What is the interpretation of independent events
Two events defined on the same sample space are independent if
one does not affect the other and viceversa
Define a random variable
A random variable is a function from a sample space S into the real numbers
What are the properties of a properly defined cdf
Limits are 0 and 1 for infinity and minus infinity
It is a nondecreasing function
F(x) is right continuous, for every x0 the limit down to x0 is F(x0)
Express theorem about pdf and if its valid or not
A Function is a pdf iff it takes non-negative values and it integrates to 1.
Define iid RVs
Two random variables are identically distributed if their cdfs coincide.
What does linearity of expectation mean
Expectation of the sum is the sum of the expectation
What is all RV’s first non central moment
Expectation of X
What is an RVs second central moment
Variance
What are the two uses of an MGF
If rvs have the same mgf they are identically distributed
The nth non central moment can be found from the mgf
