Question 4: 1. Let X1, X2, . . . ,Xn be a random sample from an Uniform distribution on [0, 9]. Find an estimator for 0 using the method of moments (2pts). Is this estimator unbiased? Explain (lpt). 2. Let X1, X2,. . . ,Xn be a random sample from a distribution with the following probability density function u?) = 0 otherwise {29295-3 a: 2 9 where 6' > 0. Find an estimator for 0 using the method of moments (2pts). Is this estimator unbiased? Explain (lpt). Question 5: Assume that lengths of newborn babies follow a normal distribution with mean ,u. The lengths (in centimetres) of seven randomly selected newborn babies are: 56 53 54 48 52 49 53 1. Perform a hypothesis test to see if the population mean length is more than 50 centimetres at the signicant level 04 = 0.05. (3pts) 2. Construct a 99% condence interval for ,u. (3pts) Question 6: A random sample of 45 cows was selected to investigate the claim that the mean weekly milk yield for cows is greater than 120 kilograms. The sample mean of weekly milk yield is 126.3 and the sample standard deviation is 24.7. Let ,u be the population mean weekly milk yield for cows. 1. Perform a hypothesis test to see if the claim is true at the signicant level or = 0.05. (3pts) 2. Construct a 90% lower condence bound for ,u. (3pts)