An internet search engine looks for a certain keyword in a sequence of independent web sites. It is believed that 15% of the sites contain this keyword. a) Let X be the number of websites visited until the first keyword is found. Please find the type of X distribution and compute the expected value and the standard deviation of X (/2) b) Out of the first 10 websites, let Y be the number of sites that contain the keyword. Please find the type of Y distribution and compute the expected value and the standard deviation of Y. (/2)

c) Please calculate the probability that at least 5 of the first 10 websites contain the keyword. (/3) d) If an investigator also wants to know the frequency of this keyword typed into the search engine, let Z be the number of times this keyword is typed into the engine for searching per 10 minutes, please find the type of Z distribution and compute the expected value and the standard deviation of Z as well as the probability of getting 2 searches of this keyword within a 10-minute time period with typical keyword searching frequency known as 0.1 per minute. (/3)