a) Consider a logic circuit with three inputs A, B and C and an output Y. Output Y is high (1) for the following conditions: i) B and C are true ii) A and C are false iii) A, B and C are true iv) A, B and C are false Write an expression for the output function Y and minimize it. b) Determine and minimize the expression for Y which is the output for the state of the bulb in the circuit below where A, B, C and D are the switches with V as the voltage. A B

In any one-minute interval, the number of requests for a popular web page is a poisson random variable with expected value 240 requests. (a) a web server has a capacity of requests per minute. if the number of requests in a one-minute interval is greater than the server is overloaded. use the central limit theorem to estimate the smallest value of for which the probability of overload is less than 0.035. note that your answer must be an integer. also, since this is a discrete random variable, don't forget to use "continuity correction". = 268 (b) now assume that the server's capacity in any one-second interval is ⌊/60⌋, where ⌊⌋ is the largest integer ≤ (this is called the floor function.) for the value of derived in part (a), what is the probability of overload in a one-second interval? this time, don't approximate via the clt, but compute the probability exactly.