IPS6eCh04_3_4bb

IPS6eCh04_3_4bb - Probability: The Study of Randomness...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
    Probability: The Study of  Randomness Random Variables IPS Chapters 4.3 and 4.4 © 2009 W.H. Freeman and Company
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Objectives (IPS Chapters 4.3 and 4.4) Random variables Discrete random variables Continuous random variables Normal probability distributions Mean of a random variable Law of large numbers Variance of a random variable Rules for means and variances
Background image of page 2
Discrete random variables A random variable is a variable whose value is a numerical outcome of a random phenomenon. A basketball player shoots three free throws. We define the random variable X as the number of baskets successfully made. A discrete random variable X has a finite number of possible values. A basketball player shoots three free throws. The number of baskets successfully made is a discrete random variable ( X ). X can only take the values 0, 1, 2, or 3.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The probability distribution of a random variable X lists the values and their probabilities: The probabilities p i must add up to 1. A basketball player shoots three free throws. The random variable X is the number of baskets successfully made. Value of X 0 1 2 3 Probability 1/8 3/8 3/8 1/8 H - H HMM HHM MHM HMH MMM MMH MHH HHH
Background image of page 4
The probability of any event is the sum of the probabilities p i of the values of X that make up the event. A basketball player shoots three free throws. The random variable X is the number of baskets successfully made. Value of X 0 1 2 3 Probability 1/8 3/8 3/8 1/8 HMM HHM MHM HMH MMM MMH MHH HHH What is the probability that the player successfully makes at least two baskets (“at least two” means “two or more”)? P ( X ≥2) = P ( X =2) + P ( X =3) = 3/8 + 1/8 = 1/2 What is the probability that the player successfully makes fewer than three baskets? P ( X <3) = P ( X =0) + P ( X =1) + P ( X =2) = 1/8 + 3/8 + 3/8 = 7/8 or P ( X <3) = 1 – P ( X =3) = 1 – 1/8 = 7/8
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
A continuous random variable X takes all values in an interval . Example: There is an infinity of numbers between 0 and 1 (e.g., 0.001, 0.4, 0.0063876). How do we assign probabilities to events in an infinite sample space? We use density curves and compute probabilities for intervals . The probability of any event is the area under the density curve for the values of X that make up the event. Continuous random variables
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 22

IPS6eCh04_3_4bb - Probability: The Study of Randomness...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online