4. The daily profit from a juice vending machine placed in an office building is a value of a random variable with unknown mean and standard deviation $ 2.10. Assume that the prior distribution of the mean daily profit is normal with mean = $30.00 and standard deviation v = $1.75. If one of these juice machines placed in a certain building showed an average daily profit of x = $24.90 during the first 30 days, find a) the Bayes estimate of the true average daily profit for this building b) The probability that the average daily profit from the machine in this building is between $24.00 and $26.00. 5. The breaking strength of a certain type of cloth is normally distributed with unknown mean but with a standard deviation equal to 3 psi. Suppose also that based on previous experience we feel that the unknown mean has a prior distribution that is normally distributed with mean 200 and standard deviation 2. If the average breaking strength of a sample of 20 specimens is 182 psi, find a) The Bayes estimate of the mean breaking strength of this type of cloth b) The probability that the mean breaking strength is between 182.5 and 185 psi 6. Let XXX, be IID Bernoulli (0), where 0 <