Statistics Formulas

Question 1

What is P(A U B)?

Answer 1

The probability of A or B occurring. It equals P(A) + P(B).

Question 2

How do you test if A and B are disjoint?

Answer 2

P(A U B) = P(A) + P(B)

Question 3

What is P(A ∩ B)?

Answer 3

The probability of A and B occurring. It equals P(A) * P(B).

Question 4

P(A’) = P(A^c) = ? and what is it?

Answer 4

The complement rule. It is used for finding the opposite of the question - i.e. if the question is asking for the probability of not rolling a 5, the complement rule is used to find the probability of rolling a 5.

P(A’) = 1 - P(A)

Question 5

What is independence?

Answer 5

Independence means that events do not affect each other. For example, hair color and nail length.

Question 6

P(A | B) is?

Answer 6

P(A | B) means the probability of A given B. This also means that A and B are not independent, as they affect each other. P(A | B) = P(B ∩ A) / P(B)

Question 7

If A and B are independent, how does P(A | B) work?

Answer 7

If events A and B are independent, then P(A | B) = P(A) and P(B | A) = P(B). Then you would just do P(A ∩ B) or P(A) * P(B).

Question 8

What are the General Multiplication Rules for 2 non-independent events?

Answer 8

P(A ∩ B) = P(A) * P(B | A)

P(B | A) = P(A ∩ B) / P(A)

Question 9

What are the 4 conditions for a Binomial Setting?

Answer 9

1) There are a fixed number N of trials.
2) Each trial is independent.
3) Each trial results in success of failure.
4) The probability of success, P, is constant.

For example, we roll a die 4 times. What is the probability that we get a ‘6’ exactly 3 times?

Question 10

How do you find the mean and standard deviation of binomial distributions?

Answer 10

m = np and S = sqrt(np(1-p)), where n is the number of trials and p is the probability of success.

Question 11

What is the formula for solving binomial distribution problems?

Answer 11

P(X) = C*p^x * (1-p)^n-x

C is the Binomial Random Variable which equals to n!/x!(n-x)!. It’s easier to just use NCR on a calculator.

Question 12

What are the 4 conditions for a geometric setting?

Answer 12

1) Each trial n results in success or failure.
2) Trials are independent.
3) The probability of success, P, is constant
4) The variable of interest is the number of trials required to obtain the first success.

For example, you roll a die until a 3 occurs. You want to know the probability that the 3 occurs on the third roll.

Question 13

What is the formula for solving geometric distribution problems?

Answer 13

P(X=n) = (1-p)^3-1 * p

Question 14

How do you find the mean and standard deviation for geometric distributions?

Answer 14

m = 1/p
S = sqrt((1-p) / p^2)