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
Reminder, in normal distribution probabilities, these do not matter
P(X<x) is the same as P(X<=x)
