Discrete and Continuous Probability Distributions
- Random variable- a function that assigns a number to each possible outcome in a random experiment
* Random variables can be classified as either discrete or continuous
* Discrete random variables- when modeling the behavior of a discrete random variable, we use a discrete probability function that can usually be expressed by a formula or table
* Probabilities must be between 0 & 1 and must sum up to 1
* Continuous random variables- when modeling the behavior of a continuous random variable, we use a continuous probability function that takes form of a curve
* Properties- the entire curve must be above the x-axis and the total area underneath the curve must be 1
* Finding probabilities- we find the area under the curve between the two endpoints of the interval - The binomial distribution is a special named discrete probability distribution that is used when the random variable only has two possible values
* The outcome of interest is referred to as a success
* 0 typically represents failure and 1 represents success
* Conditions of binomial distributions:
* Fixed number of trials
* Two possible outcomes (success or failure)
* The probability of success, p, is the same for each trial
* Trials are independent (the outcome of one trial does not affect other trials)
* Parameters- key pieces of identifying information for distributions
* n=number of trials
* p=probability of success
* The shape of the binomial distribution depends on the number of trials (n) and the probability of success (p)
* E(x)=n*p - Normal distribution parameters
* Mean
* Standard deviation