Midterm 1 ECON 249 Stats

complement P(A^C)

1-P(A)

random experiment (discrete RV)

Outcome of an unknown experiment. P(X=x)=f(x)

mutually exclusive P(A or B)

P(A or B ) = P(A) + P(B) P( A intersect B) = 0

non disjoint events P(A or B)

P(A or B ) = P(A) + P(B) - P(A intersect B)

independent events P(A intersect B)

P(A) x P(B)

conditional probability P(A|B) and P(B|A)

P(A|B) = P(A intersect B)/ P(B) P(B|A) =P(A intersect B)/ P(A) remember that you can also solve for P(A intersect B) if you use the multiplication rule

independent events conditional probabilities P(A|B) and P(B|A)

P(A|B) = P(A) P(B|A) = P(B)

continuous random variable

P(X=x) does NOT equal f(x)

law of total probability

tool to relate marginal to conditional probabilities P(A) = P(A interesect B) + P(A intersect B^C) P(A) = P(A|B) * P(B) + P(A|B^c) * P(B^c)

z-score

xi-x̅ /s

sample mean

x̅ = Σxi / n can be rearrange to x̅*n = Σranging questions xi to solve some of the rear

population variance

Σ(xi-mu)^2/N

sample variance

Σ(xi-x̅)^2/n-1

weighted mean

Σxiwi / Σwi

uniform distribution (continuous random variable)

events are equally likely of occurring and continuous can't find exact probability at one point height: 1/(b-a) entire interval lenght (b-a) what we are specifically looking at.

expected value and variance for binomial

expected value = np variance = np(1-p)

expected value and variance for bernoulli

expected value = p variance = p(1-p) *the formulas are the same as before but it just so happens that we get p and p(1-p) when using bernoulli

expected value and variance for RV

expected value = Σx * P(x) variance = Σ(x -mu)^2* P(x)

expected value and variance for poisson

expected value = λ variance =λ can be scale to time, r is lambda multiply by t

if skewed right (tail to the right)

mean > median

if skewed left (tail left)

median > mean

sum of a constant Σxi is...

n * xi

permutation

n!/(n-x)! order matters

combination

n!/(n-x)!x! order does not matter

coefficient of variation population

o (standard deviation of population)/ mu(population mean) x 100

poisson distributions

probability of a given number of events happening in a period of time f(x) = (λ^x e^-λ)/x!

bernoulli trial

random experiment with two outcomes (success/failure) f(x)= p^x(1-p)^1-x

binomial distributions

repeated bernoulli experiment (lets say it says smt among the lines of success/failure, then says we sample 5 ppl - binomial) f(x)= (n,x)p^x(1-p)^n-x

coefficient of variation sample

s (standard deviation of mean)/x (sample mean)

population standard deviation

square root of Σ(xi-mu)^2/N

sample standard deviation

square root of Σ(xi-x̅)^2/n-1