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