I'Iil 2 10 5:} Conditioned on a given value A = a, random variable K is Poisson distributed with expected value a. If A is exponentially distributed, fA(a) = 363\" for a 2 0, what is the expected value of K? 03 01/3 0 There is no closed form answer. \f10 5 4 10 9 Which of the following statements are true: O Independent Gaussians are uncorrelated. O Uncorrelated Gaussians are independent. O Uncorrelated Gaussians are independent if and only if they are zero-mean.Random variables (Iii, i = 1, 100 are independent, and each is distributed uniformly on the interval [0, 271']. If Y = 23:? cos (13,-, the variance of Y is O 1/ 100 050 o 100 X is exponentially distributed with mean value 60. What is the expected value of X conditioned on the event {X E [70, 73] }? 0 approximately 60 0 none of the offered answers 0 approximately 71.5 A local store has purchased M = 1000 10-gallon buckets of milk, each from a different farm. Before bottling the milk and putting it up for sale, the store has to test the milk for harmful bacteria. Each farm's milk is affected by the bacteria independently and in the same manner, such that the probability of a bucket containing bad milk is Pg, = 0.01. Testing can be performed bucket-by-bucket, or several buckets can be poured into one larger container and the entire container then tested. The price of testing is $10 per test, regardless of the size of the container. If a container tests positive for the presence of harmful bacteria, it must be discarded. The good milk is sold for $3 per gallon. Which of the following statements are true: [3 From the viewpoint of expenditures, is it better to pour all the milk into a single container and perform one test. C] From the viewpoint of expenditures, is it better to perform testing bucket-by-bucket. [3 From the viewpoint of maximizing the yield of good milk, is it better to perform testing bucket-by- bucket. C] From the viewpoint of maximizing the yield of good milk, is it better to pour all the milk into a single container and perform one test. In the previous problem, if all the milk is divided into K = M/N containers (an integer number), each holding N buckets, evaluate the average yield (number of buckets) of good milk. How much money is spent on testing in this case? How much is earned on average from selling the good milk? If N = 10, which of the following statements are true: C] If each bucket were tested independently, the average sales would have been $19,700. [3 If each bucket were tested independently, the average yield would have been 1,200 buckets. C] None of the statements are true. C] If each bucket were tested independently, the average sales would have been $29,700. C] The average earnings are $27,000. C] The average earnings are $26,000. C] The average number of good buckets is approximately 900