Q1. Determine the value of c and the covariance and correlation for the joint probability mass function fxy = c (x + y) for x = 1,2,3 and y = 1,2,3. Q2. If the lifetime X of a hearing aid battery has Weibull distribution with a = 0.1, p = 0.5. Find the probability that such a battery a) will function for more than 300 hours b) will not last 100 hours Also, Find c) mean d) variance Q3: Suppose that the diameter of meter shafts in a lot have a mean of 0.249 inches and standard deviation of 0.03 inches. The inner diameter of bearings in another lot have a mean of 0.255 inches and standard deviation of 0.002 inches. a) Find the mean and standard deviation of clearances between shafts and bearings selected from these lots. b) If a shaft and bearings are selected at random, find the probability that the shaft will not fit inside the bearings. Assume that both dimensions are normally distributed. Q4. The heat evolved in calories per gram of a mixture cement is approximately normally distributed. The mean is thought to be 100 and the standard deviation is 2. We wish to test Ho: u = 100 versus H (Not = 100 ) with a sample of n = 7 specimens. a) If the acceptance region is defined as 98.5 Q1. Determine the value of c and the covariance and correlation for the jointprobability mass function fxy = c(x + y) for x = 1,2,3 and y = 1,2,3.Q2. If the lifetime X of a hearing aid battery has Weibull distribution witha = 0.1,B = 0.5. Find the probability that such a batterya) will function for more than 300 hoursb) will not last 100 hoursAlso, Findc) meand) varianceQ3: Suppose that the diameter of meter shafts in a lot have a mean of 0.249 inches andstandard deviation of 0.03 inches. The inner diameter of bearings in another lot have amean of 0.255 inches and standard deviation of 0.002 inches.a) Find the mean and standard deviation of clearances between shafts and bearingsselected from these lots.b) If a shaft and bearings are selected at random, find the probability that the shaft willnot fit inside the bearings. Assume that both dimensions are normally distributed.Q4. The heat evolved in calories per gram of a cement mixture is approximatelynormally distributed. The mean is thought to be 100 and the standard deviation is2. We wish to test Ho: u = 100 versus H1: µ 100 with a sample of n = 7specimens.a) If the acceptance region is defined as 98.5

Question

Q1.  Determine the value of c and the covariance and correlation for the joint probability mass function fxy = c (x + y) for x = 1,2,3 and y = 1,2,3.  Q2.  If the lifetime X of a hearing aid battery has Weibull distribution with a = 0.1, p = 0.5.  Find the probability that such a battery a) will function for more than 300 hours b) will not last 100 hours Also, Find c) mean d) variance Q3: Suppose that the diameter of meter shafts in a lot have a mean of 0.249 inches  and standard deviation of 0.03 inches.  The inner diameter of bearings in another lot have a mean of 0.255 inches and standard deviation of 0.002 inches.  a) Find the mean and standard deviation of clearances between shafts and bearings selected from these lots.  b) If a shaft and bearings are selected at random, find the probability that the shaft will not fit inside the bearings. Assume that both dimensions are normally distributed.  Q4.  The heat evolved in calories per gram of a mixture cement is approximately normally distributed.  The mean is thought to be 100 and the standard deviation is 2. We wish to test Ho: u = 100 versus H (Not = 100 ) with a sample of n = 7 specimens.  a) If the acceptance region is defined as 98.5 Q1. Determine the value of c and the covariance and correlation for the jointprobability mass function fxy = c(x + y) for x = 1,2,3 and y = 1,2,3.Q2. If the lifetime X of a hearing aid battery has Weibull distribution witha = 0.1,B = 0.5. Find the probability that such a batterya) will function for more than 300 hoursb) will not last 100 hoursAlso, Findc) meand) varianceQ3: Suppose that the diameter of meter shafts in a lot have a mean of 0.249 inches andstandard deviation of 0.03 inches. The inner diameter of bearings in another lot have amean of 0.255 inches and standard deviation of 0.002 inches.a) Find the mean and standard deviation of clearances between shafts and bearingsselected from these lots.b) If a shaft and bearings are selected at random, find the probability that the shaft willnot fit inside the bearings. Assume that both dimensions are normally distributed.Q4. The heat evolved in calories per gram of a cement mixture is approximatelynormally distributed. The mean is thought to be 100 and the standard deviation is2. We wish to test Ho: u = 100 versus H1: µ 100 with a sample of n = 7specimens.a) If the acceptance region is defined as 98.5

Accepted Answer

Hello. Since your question has multiple parts, we will solve first question for you. If you want…