{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2010100AHW2

# 2010100AHW2 - state 1 Each time he stays where he is with...

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

STAT 100A HWII Note (1) Rule of total probability. Suppose B 1 , B 2 , ..., B n partition the sample space, then P ( A ) = n i =1 P ( A B i ) = n i =1 P ( B i ) P ( A | B i ). (2) Bayes rule. P ( B j | A ) = P ( B j A ) /P ( A ) = P ( B j ) P ( A | B j ) / n i =1 P ( B i ) P ( A | B i ). Please show all the necessary steps in your calculations. Please be precise with notation. Problem 1: Suppose an urn has b blue balls and r red balls. We randomly pick a ball. If the ball is red, we put two red balls back to the urn. If the ball is blue, we put two blue balls back to the urn. Then we randomly pick a ball again. (1) What is the probability that the first pick is red? (2) What is the probability that the second pick is red? (3) (Optional) If we continue, then what is the probability that the third pick is red? Problem 2: Suppose a person performs a random walk over three states, 1, 2, 3. He starts from
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: state 1. Each time, he stays where he is with probability 1/2, and he moves to each one of the other two states with probability 1/4. Let X t be the state of this person at time t , and X = 1. (1) What is the distribution of X 1 , i.e., what is the probability that X 1 = k for k = 1 , 2 , 3? (2) What is the distribution of X 2 ? (3) (Optional) What is the distribution of X 3 ? Problem 3: Suppose at any moment, the probability that there is ﬁre in a classroom is α . If there is a ﬁre, the probability we hear the ﬁre alarm is β . If there is not a ﬁre, the probability that there is ﬁre alarm is γ . Given that we hear the ﬁre alarm, what is the probability that there is ﬁre? 1...
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