Binomial Random Variable

z score

observed μ/σ

poisson probability

p(x)= (μ² x e^-μ)/x!

Poisson max min

μ+2σ, μ-2σ

When to use binomial coefficient

whenever you need to count combinations, not arrangements

You’re choosing a group of items, but order doesn’t matter.

Example: Choosing 3 students from a class of 10.

That’s |10

            3|

binomial coefficient formula

(n k​)= n!/(k!(n−k))

mean binomial sign

µ micron sign

µ formula

µ= n x p

Standard deviation binomial

σ = sqrt(np(1-p))

Bermoulli Random Variable

B (1, p) comes from n independent Bermoulli trials

Binomial Probability Function Formula

P(X=k)=(n k​)p^k(1−p)^n-k

mean (expected value) formula for a probability distribution

μ=∑^x⋅p(x)

when to use mean (expected value) formula for a probability distribution

whenever you have a discrete random variable (like rolling dice, coin flips, number of patients, etc.) and you want to find its average outcome in the long run

Discrete random variable formula (variance)

σ²=∑(x−μ)²p(x)

discrete random variable vs. binomial distribution

Roll a die → the number showing (1, 2, 3, 4, 5, 6)

any situation where the outcomes are numbers you can list

binomial distribution

special kind of discrete random variable.

You want to know how many successes you get.

when to use permutations

no repetition and order matters

permutation formula

p(n,k)= n!/(n-k)!

conditonal probability

P(A∣B)= P(A∩B)​/P(B)

• Pick a card from a deck.

• What’s the probability it’s a King given it’s a face card?

P(King∣Face)= (4/52​)/(12/52) =1/3

bayes’ theorem

P(A∣B)= (P(B∣A)⋅P(A)​)/P(B)When to use

When to use Baye’s theorem

Use when you need to flip the condition around (you know P(B∣A), but you want P(A∣B)

sd poisson

sqrtμ