Graph a discrete probability distribution

Learning Objectives Define a discrete random variable and its probability distribution. Construct a probability distribution table for a given discrete random variable. Verify that a function or table represents a valid probability distribution. Graph a discrete probability distribution using a histogram or bar chart. Interpret the key features of a graphed distribution, such as its shape and center. Calculate the expected value (mean) of a discrete random variable from its distribution table. Use a graphed distribution to determine the probability of an event. Ever wondered what the chances are of winning different prizes in a carnival game? 🎡 Graphing probabilities can help you see if the game is truly in your favor! This tutorial will teach you how to take a set of ou...

TermDefinitionExample Discrete Random VariableA variable, typically denoted by X, that can take on a finite or countably infinite number of distinct values. These values are often integers that result from counting something.Let X be the number of heads obtained when flipping a coin three times. The possible values for X are {0, 1, 2, 3}. Probability DistributionA table, formula, or graph that describes the probability for each possible value of a random variable.For a single fair die roll, the distribution table would list the outcomes {1, 2, 3, 4, 5, 6} and the probability for each, which is 1/6. Probability Mass Function (PMF)A function, denoted P(X = x), that gives the probability that a discrete random variable X is exactly equal to some value x.If X is the result of a fair die roll,...

Conditions for a Valid Probability Distribution 1. 0 ≤ P(X = x) ≤ 1 for all values of x. \n 2. Σ P(X = x) = 1 These two conditions must be met for any discrete probability distribution. The first rule states that every probability must be between 0 and 1, inclusive. The second rule states that the sum of the probabilities for all possible outcomes must equal 1. Formula for Expected Value (Mean) μ = E[X] = Σ [x * P(X = x)] To calculate the expected value, you multiply each possible value (x) of the random variable by its corresponding probability P(X = x), and then sum all of these products together.