16\.\* Show that a. sin( π 2 + iy) = 1 2 (ey + e−y ) = cosh y b. |sin z| ≥ 1 at all points on the square with vertices ±(N + 1 2 )π ± (N + 1 2 )πi, for any positive integer N. c. |sin z|→[infinity], as Imz = y → ±[infinity].

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?