Unit 4:Random variables and probability distributions
Definitions:
A random variable : a numerical measure of the outcome of a probability experiment, so its values are determined by chance. Random variables are typically denoted using a capital letter such as x
Continuous random variables: variables that can be measured such as weight of M&Ms of length of babies
-infinitely many values. -can be plotted on a number line in an uninterrupted fashion
Discrete random variables: variables that can be counted such as the number of red M&Ms.
-finite or countable number of values
-can be plotted on a number line with space between each point
-use S.O.C.S
​
​
Probability distribution of the random variable x is the distribution of values and their corresponding probabilities. It is represented using a table, graph or mathematical model.
Probability histogram: to graph the probability distribution of a discrete random variable, construct a probability histogram
Binomial experiment: 4 conditions must be met
-only 2 outcomes:success(p),failure (q)
-probability of success for all trials
-trials are independent
-there are a fixed number of trials
Binomial distribution: the random variable, X, will count the number of successes in a certain number of trials (n)
-X(# of successful trials) has a Binomial Distribution
-n=number of trials
-p=probability of success on any one trial
-short hand+ X is B(n,p)
Combinations:
​
​
Formula for probability:
​
​
​
Calculator:
​
Geometric Distribution: goal is to find the probability of the first success occurring during the nth trial
4 requirements for geometric distribution:
-each observation falls into either success or failure
-probability of success (p) is same for each observation
-observations are independent
-variable of interest is # of trials required to obtain the first success
Formula:
​
​
​
​
​
​
​
​
Probability that it takes more than n trials to achieve success:
p(x>n)=(1-p)^n
​
​
​
​
​
​
​
​
​
​
​
​
​
​
​
​
