We can use a random number generator to estimate probabilities that might otherwise be difficult to evaluate. Consider the probability of obtaining four heads on four flips. Generate four separate random experiments of 0s and 1s representing N trials each. (You can do this by generating an Nx4 random array rather than an Nx1 array as in #1.) Now look at the corresponding rows and determine what percentage of the time all four coin flips across a row are heads (all entries equal 1). Show how you do this in MATLAB. Report the percentage with N=10,000 and 100,000, and compare this to the expected percentage.

Suppose you are an ad-serving company and you maintain a log of cookie data for ads you serve to the web pages for a particular vendor (say amazon). a. how can you use this data to determine which are the best ads? b. how can you use this data to determine which are the best ad formats? c. how could you records of past ads and ad clicks to determine which ads to send to a given ip address? d. how could you use this data to determine how well the technique you used in your answer to part c was working? e. how could you use this data to determine that a given ip address is used by more than one person? f. how does having this data give you a competitive advantage vis-à-vis other ad-serving companies?