Stats M. 4 Flashcards
random variable
a function that assigns a number to each possible outcome in a random experiment (Let X=)
-can be classified as discrete or continuous)
discrete
if the set of all possible values is a separate set of numbers
continuous
if the set of all possible values is an interval of number
discrete probability function
-all probabilities must be between 0 and 1
-must all sum to 1
expected value of a discrete random variable
used to measure center (mean) of the probability distribution (long run average)
-multiply each possible value by its corresponding probability and then summing up all the products (does not need to be between 0 and 1)
-E(x)
binomial distribution
-two possible values
-0=failure, 1=success
binomial distribution conditions:
- a fixed number of trials
- each trial has w possible outcomes (success and failure)
- the probability of success is the same for each trial
- the trails are independent (don’t affect each other)
Binomial distribution parameters
N= number of trials
P= probability of success
X~Bin(n, p)
expected value of a binomial distribution
E(x)=NxP
Reminder, in binomial distribution, these matter…
P(X<x) is NOT the same as P(X<=x)
Normal Distributions
-continuous probability function
-curve must be above x-axis and total area underneath the curve must be 1
Normal distribution parameters
mean (u shaped)
standard deviation (o shape)
X~N(u,o)
The larger the standard deviation…
the less narrow the curve
the smaller the standard deviation…
the more narrow the curve
changing the mean affects…
where the distribution is centered
