Let x denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. suppose the pdf of x is f(x; u) 55(u 1 1)xu 0 # x # 1 0 otherwise where 21 , u. a random sample of ten students yields data x1 5 .92, x2 5 .79, x3 5 .90, x4 5 .65, x5 5 .86, x6 5 .47, x7 5 .73, x8 5 .97, x9 5 .94, x10 5 .77. a. use the method of moments to obtain an estimator of u, and then compute the estimate for this data. b. obtain the maximum likelihood estimator of u, and then compute the estimate for the given data.

Television viewing reached a new high when the global information and measurement company reported a mean daily viewing time of 8.35 hours per household. use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household. a. what is the probability that a household views television between 4 and 10 hours a day? (to 4 decimals) b. how many hours of television viewing must a household have in order to be in the top 7% of all television viewing household? (to 2 decimals) c. what is the probability that a household views television more than 4 hours a day? (to 4 decimals)