DESCRIPTION Please keep in mind the OMSI rules. Save your files often. Submit each answer individually and make sure you receive the notification of successful submission. Don't wait till the last moment to submit all answers, as there might be network traffic in the last 5 minutes causing unexpected delay and failure. Remember that clicking CopyQtoA will copy the entire question box to the answer box. In questions involving code which will PARTIALLY be given to you in the question specs, you may need to add new lines. There may not be information given as to where the lines should be inserted. MAKE SURE TO RUN THE R CODE ANSWER IN PROBLEMS THAT INVOLVE R CODE! QUESTION (Text answer - 20 pts) An example in lecture concerning computer recognition in medical images. What disease was of interest there? And what kind of probability was this an example of? QUESTION (Text answer - 20 pts) For two events A and B, if we write P(A and B) = P(A)P(B), what assumption are we making? QUESTION (Text answer - 20 pts) Eqn. (2.8) gives a "mailing tube" for finding conditional probabilities; but often we get those probabilities from intuition rather than from this formula; give an example of this in the book QUESTION (Text Answer - 20 pts) E(XY) = E(X)E(Y) if X and Y are independent. True or False? QUESTION (Text answer - 20 pts) We say the mean and median are ways to quantify the notion of "central tendency." What is the corresponding term for variance? QUESTION -ext .R -run 'Rscript ./omsi_answer6.R' (R code answer - 20 pts) In the bus ridership problem, sec 2.11 (page 20), let's say the bus has a limit of 4 passengers and we are told that the bus left stop 1 with 2 passengers. What is the proability that when the bus is leaving stop 2, it has reached its limit? QUESTION -ext .R -run 'Rscript ./omsi_answer7.R' (R code answer - 20 pts) In the Preferential Attachment Graph Model example, sec 2.13.1 (page 24) what is the proability that after v_5 joins the graph has a structure of a chain i.e each node has degree less than or equal to 2. QUESTION -ext .R -run 'Rscript ./omsi_answer8.R' (R code answer - 20 pts) If X and Y are two independent die rolls, what is the support of (X-Y)? print(c( )) QUESTION -ext .R -run 'Rscript ./omsi_answer9.R' (R code answer - 20 pts) We toss a coin repeatedly until we see the pattern "HTH". Let N denote the number of tosses needed, e.g. for sequence HTTHTH, N=6 Modify the code in sec. 2.14.11 to find approximate probability of N > m. Original code is as below: ngtm <- function (k,m, nreps ) { count <- 0 for (rep in 1: nreps ) { consech <- 0 for (i in 1:m) { toss <- sample (0:1 ,1) if ( toss ) { consech <- consech + 1 if ( consech == k) break } else consech <- 0 } if ( consech < k) count <- count + 1 } return ( count / nreps ) } QUESTION -ext .R -run 'Rscript ./omsi_answer10.R' (R code answer - 20 pts) In the Monty Hall problem, say there are 4 doors and 3 goats. Find the value of the numerator in Eqn. (3.1).