Let Y be a Bernoulli random variable with success probability Pr ( Y = 1 ) = p , and let Y 1 , … , Y n be i. i.d. draws from this distribution. Let ˆ p be the fraction of successes (1s) in this sample. Show that ˆ p = ¯¯¯ Y . Show that ˆ p is an unbiased estimator of p. Show that var ( ˆ p ) = p ( 1 − p ) / n .

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d.what is the height of the tide after 93 hours?