Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Transcript

AP STATISTICS Section 7.1 Random Variables Objective: To be able to recognize discrete and continuous random variables and calculate probabilities using them. A Random Variable is a variable whose value is a numerical outcome of a random event. Denoted using capital letters: X, Y, … Ex. X = sum of 2 dice A discrete random variable has a countable number of possible outcomes. A probability distribution is a table that assigns probabilities to outcomes of a discrete random variable. General Probability Table: X=𝒙𝒊 𝒙𝟏 𝒙𝟐 … 𝒙𝒏 P(X=𝒙𝒊 ) 𝑝1 𝑝2 … 𝑝𝑛 ** Last row is optional. Only include it if asked to do so. F(X=𝑥𝑖 ) is the cumulative density function. F(X=𝑥𝑖 ) = P(X ≤ 𝑥𝑖 ) Every Probability Distribution must meet 2 requirements: 1. Every 𝑝𝑖 is between 0 and 1. 2. The 𝑝𝑖 = 1 Ex. Create the probability distribution for the random variable X where X = the sum of two dice. Then answer the following questions. (X=𝑥𝑖 ) P(X= 𝑥𝑖 ) Find P(X=7 or 11) = Find P(X = 2 or 3 or 12)= The best way to display a probability distribution is through the use of a __________________________. Ex. Create a probability distribution for the random variable X where X = the number of times a head is observed when a coin is tossed 3 times. REVIEW DENSITY CURVES: 1. 2. Z-SCORES: A continuous random variable takes on all values of that random variable in an interval of numbers. • The probability distribution of a continuous random variable is described by a density curve. • The area under the curve represents the probability of the said event occurring. • Continuous random variables are measured while discrete are counted. Ex. Let X~U(0,2) a. Sketch this density curve. b. Find P(X < 1) c. Find P(X ≤ 1) d. Find P(0.5 < X < 1.6)