Statistical Distribution Flashcards
Random variable
A variable that takes different values with different probabilities
Discrete random variables
Can only take a certain number of values
X
A discrete random variable
x
The particular values the random variable can take
Uniform distribution
A distribution where each outcome is equally likely
Probability Distribution
Each outcome and the likelihood of achieving it
F(x)
The cumulative distribution function, adding up the probabilities of x and all x values lower than it
F(x) = P(X <= x)
Solving problems where F(x) is a function
F(xmax) = 1
Combinations vs permutations
Order is important in permutations but isn’t in combinations
How many ways to order x of n items if repetition is allowed
n^x
How many ways to arrange n items if repetition isn’t allowed
n!
Ordering x of n items
n!/x!
Ordering n items if x of n are identical and the other’s aren’t
n!/x!
The number of ways of ordering n items of one type and n-x items of another type
n choose x
Binomial conditions
- There are a fixed number of trials, n
- Each trial has outcomes success (p) or failure (1-p)
- All trials are independent
- The probability of success if the same in each trial
- The variable is the total number of successes in the X trials
