Exam 2 Flashcards
(19 cards)
What is the formula for conditional probability?
P(A/B) = P(A ∩ B) / P(B)
Independent Events must satisfy:
P(A/B) = P(A)P(B)
P(A/B) = P(A)
One event does not affect the probability of another event happening
Bayes Theroem:
P(A/B) = P(B/A)P(A) / P(B)
or: AB-BAAB
Discrete Values are:
Countable
Continuous Values are:
Not Countable
What is the combination formula?
(n, r) = n! / r!(n-r)!
P(A U B) = what property?
P(A U B) = P(A) + P(B) - P(A ∩ B)
What is the multiplication rule for 2 events? P(A ∩ B) = …
P(A ∩ B) = P(B/A)P(A)
What is the law of total probability?
P(B) = …
P(B) = P(A1)P(B/A1) + … + P(Ak)P(B/Ak),
Ak for entire population
The multiplication rule:
P(A ∩ B) = P(B/A)P(A)
Can be reversed as:
P(A ∩ B) = …
P(A ∩ B) = P(A/B)P(B)
What function do we use to find P(X <= x)?
The CDF: F(x), is used to find: P(X <= x)
What function is non-decreasing?
The CDF, F(x)
How do you find the PDF from the CDF?
The PDF, f(x) is found by taking the derivative of the CDF, F(x).
How do you find the CDF from the PDF?
The CDF, F(x) is found by integrating the PDF, f(y), with lower bound -inf (lowest val), and upper bound, x. Remember the y.
What function is used to find P(a < X < b)?
The PDF, f(x). Integrate using lower bound a and upper bound b.
What makes a PDF legit?
The total area under the PDF curve must be 1. The PDF is non-negitave.
How do we find P(X >= x)?
P(X >= x) = 1 - F(x)
where F(x) is a CDF function.
Is PMF function discrete or continuous?
Discrete
