{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 6 Notes (1)

# Chapter 6 Notes (1) - *4 ~14 6 Probability Distributions...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: *4 ~14 6 Probability Distributions 3.1 Summarizing Possible Outcomes and Their Probabilities Random Variable A random variable is a numerical measurement of the outcome of a random phenomenon. Often, the randomness results from the use of random sampling or a randomized Experiment to gather the data. Exllz Number of touchdowns for Red Raiders, Duration of a call Probability Distribution The probability distribution of a random variable speciﬁes its possible vnluai and their probabilities. Ex]: Probability distribution of number of home runs in a game for Boston Red Sox. The table lists the possible values for the number of home runs and the corresponding probabilities. Number ol' Home Runs Probability 0 0.23 1 0.38 2 0.22 3 0.13 4 0.03 5 0.01 6 or more T Probability dimrilmtions can be deﬁned for both discm random variables and continuous random variables. We will ﬁrst look at discrete random WTlelkS, Probability Distribntlon of 3 Discrete Random Variable A discrete random tunable X takes a set of separate values (such as 0.1.1....) Its probability distribution assigns a probability P(r) to each possible value at z. . For each z, the probability 13(1) ialls between a and i. I The sum of the prubnbilities {or all [he pmzible x valum equals 1. Ema: Refer to Exz. . for each 1. the probability huh between 0 ml 1. (all the vnlnm 0.23, 0.33, 0.22, 0.13, 0.03, ml 0.01 are between 0 ml 1) . sum or the probabilities for all the possible a: value equals 1. (0.23 + 0.33 + 0.22 + 0.13 + 0.03 + 0.01:1) Therefore, it is a probability distribution. Probability of at least 3 humernns is P(X 3 3) = P(3) + Pu) + 11(5) + [’(6) = 0.13 + (Loo +0.01Jr 0.00 = 0.17 an m n a n u an n' a 'l 1 . a I : l 1 -. Figure 1; Probability Distribution for Ex.2 ExA: F‘mm six marbles numbered as l,1,1,1,2,2. lwu marblm will be drawn at. mt (loin without replacement. Let X denote the sunle of the numbers on the selected marbles. List the possible values of X and determine the probability distribution. Outcome Pmbl bility 3/5 ®© Nola/5) = 61:5 l‘lﬁllﬂﬁl = #115 (lellllsl - 1/15 lzléluls) . 1/15 ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern