Let x be the number of photons counted by a receiver in an optical communication system. it is known that x is a poisson random variable with rate λ1 when a signal is present and a poisson random variable with rate λ0 < λ1 when a signal is absent. the probability that the signal is present is p. suppose that we observe x = k photons. we want to determine a threshold t such that if k ≥ t then we claim that the signal is present; and if k < t then we claim that the signal is absent. what is this t?

Using the given statements, state whether the conditional statement is true or false. p: 7 + 1 = 0 q: 2 + 2 = 5 is p q true or false?

The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. complete parts (a) and (b) below. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is nothing. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is nothing. (round to three decimal places as needed.)

Ascientist places 24 cells in a petri dish. she knows the cells grow at an exponential rate, doubling in number every hour. how long will it take (in hours) for there to be 1100 cells in the dish? time to 1100 cells: 5.51832530 hours how long will it take to reach 110 cells? time to 110 cells : 2.1963972 hours what is the average rate of change in the number of cells between 9 hours and 11 hours? average rate of change: cells per hour what is the instantaneous rate of change after 7 hours? instantaneous rate of change: cells per hour note: you can earn partial credit on this problem.