Auto claim sizes follow a gamma distribution with mean 500 and mode 250. Claim sizes are independent of each other. Assuming there will be 10 claims next year and using the normal approximation, calculate the probability that the sum of losses next year will exceed 6,000. A 0.19 в 0.29 с 0.39 D 0.49 E 0.61

Suppose that the weight of an newborn fawn is Uniformly distributed between 2.2 and 3.9 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible. The mean of this distribution is   . The standard deviation is   . The probability that fawn will weigh exactly 2.5 kg is    P(x=2.5)=P(x=2.5)=   . The probability that a newborn fawn will be weigh between 2.6 kg and 3.7 kg is    P(2.6<x<3.7)=P(2.6<x<3.7)=   . The probability that a newborn fawn will be weigh more than 3.24 kg is    P(x>3.24)=P(x>3.24)=   . P(x>2.8∣x<3.3)=P(x>2.8∣x<3.3)=   . Find the 45th percentile.   kg

Suppose the mean monthly return on a T-Bill is 0.5% with a standard deviation of 0.58%. Sup-pose we have another investment Y with a 1.5% mean monthly return and standard deviationof 6%. Which of the two investments o ers less risk in terms of investment.

The time between failures of our video streaming service follows an exponential distribution with a mean of 40 days. Our servers have been running for 17 days, What is the probability that they will run for at least 97 days? (clarification: run for at least another 80 days given that they have been running 17 days). Report your answer to 3 decimal places.