U NIT 6 – C HAPTER – Discrete and Continuous Random Variables

D O YOU REMEMBER ? What is a probability distribution?

E XAMPLE : F LIPPING O UT ! Below is a probability distribution for flipping a coin four times and counting how many heads we see: The number of heads we see is our Random Variable. In this problem we called it “X.” Remember that a distribution shows what is possible and how often. X01234 P(X)1/164/166/164/161/16

D EFINITIONS A random variable takes numerical values that describes the outcomes of some chance process. The probability distribution of a random variable gives its possible values and their probabilities. X01234 P(X)1/164/166/164/161/16

D ISCRETE R ANDOM V ARIABLE A discrete random variable X takes a fixed set of possible values with gaps between. For example: grades on the AP test (1, 2, 3, 4,5)

D ICE, D ICE E VERYWHERE ! Come grab a die from me. Roll the die 20+ times, recording your results as you go Find the average and standard deviation for your die rolls Record your mean and standard deviation Share your mean and standard deivation them on the board

E XPECTED V ALUE (M EAN )

E XAMPLE : A B LAST FROM THE P AST X12345 P(X)

P RESS YOUR LUCK : On an American roulette wheel there are 38 slots numbered 1 through 38. Slots are numbered (half red half black) and two extra slots are labeled 0 or 00 and are green. If a player places a $1 bet on “red” the probability distribution for their net gain is as follows: Find the expected value for net gain. Value-$1$1 Probability20/3818/38

S TANDARD D EVIATION ( AND V ARIANCE ) OF A D ISCRETE R ANDOM V ARIABLE

E XAMPLE : A B LAST FROM THE P AST … A GAIN X12345 P(X)

P RESS YOUR LUCK … A GAIN : Using the same roulette example, find the standard deviation for net gain, when betting $1 on red: Value-$1$1 Probability20/3818/38

C ONTINUOUS R ANDOM V ARIABLE A continuous random variable, X, takes all values in an interval of numbers. The probability distribution of X is described by a density curve. The probability of any event is the area under the density curve and above the values of X that make up the event. For example – heights of all people in this room

Y OU DECIDE ! D ISCRETE OR C ONTINUOUS ? Time it takes you to clean your room How much it costs for dinner Inches of rainfall last month Your birthday The outcome of the roll of a dice

H OMEWORK P. 353: 2-8 even, 9, even, 21-30