DA2 formulas

Question 1

For mutually exclusive events, How do you work out probabilities?

Answer 1

P(b) + P(a) = 1 so use this to calculate all other probabilities

Question 2

How do you calculate the total number of outcomes?

Answer 2

number of outcomes ^ (number of joint attempts)

E.g. 3 coins flipped, two outcomes means its 2^(3)

Question 3

What does the addition rule state?

Answer 3

P(A/\B) = P(A) + P(B) - P(AUB)
P(AUB) = P(A) + P(B) - P(A/\B)

Question 4

What is the multiplication rule?

Answer 4

If events are independent:

P(A/\B) = P(A) * P(B)

Question 5

What is the conditional probability formula?

Answer 5

P(B|A) = P(A/\B)/P(A)

Question 6

What is the multiplication rule for dependent events?

Answer 6

P(A/\B) = P(A|B) * P(B)
P(A/\B) = P(B|A) * P(A)

Question 7

What is P(A/\B) for independent events?

Answer 7

P(A) * P(B)

Question 8

What does Bayes theorem imply?

Answer 8

P(A|B) = P(A/\B)/P(B)

Question 9

How do you calculate the variance of a rv?

Answer 9

Var(X) = (x-u)^2 * P(X)

Question 10

How do you calculate the mean of a set of random variables?

Answer 10

• Take X * P(X) for all values
• Sum them
• That is Mean/E(X)

Question 11

What is the formula for the probability function of a binomial distribution?

Answer 11

P(x) = nCx * (P)^x * (1-P)^n-x

• n = number of trials
• x = number of desired successes
• P = probability of single trial success

Question 12

What is the formula for the probability of a Poisson distribution?

Answer 12

P(x) = (u^(x) * e^(-u))/X!
Var(x) = u

Question 13

How do you calculate the probability for any normally distributed variable? X~N(u,var^2)

Answer 13

• find x-u/var(x)

- Find that value on the statistical table