We model the random amount of time (in hours) it takes to receive tech support with the probability density function f(t)=e, t> 0. We are uncertain about the rate parameter A (which gives the average number of customers served per hour), and give it a Gamma prior distribution with parameters a = 8 and ẞ = 0.5. A random sample of 4 customers yields service times of: t₁ = 0.3, t2 = 0.1, t3 = 0.5, t4 = 0.3. Compute the posterior distribution for A.
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- The weekly amount of downtime Y (in hours) for an industrial machine has approximately a gamma distribution with a = 3 and ß = 2. The loss L (in dollars) to the industrial operation as a result of this downtime is given by L = 20Y + 3Y2. Find the expected value and variance of L. E(L) = $ V(L) =Nonpoint source loads are chemical masses that travel to the main stem of a river and its tributaries in flows that are distributed over relatively long stream reaches, in contrast to those that enter at well-defined and regulated points. An article suggests that for a certain time period and location, X = nonpoint source load of total dissolved solids could be modeled with a lognormal distribution having mean value 10,249 kg/day/km and a coefficient of variation CV = 0.40 (cv = 'x Hx' In USE SALT (a) What are the mean value and standard deviation of In(X)? (Round your answers to four decimal places.) mean value standard deviation (b) What is the probability that X is at most 15,000 kg/day/km? (Round your answer to four decimal places.) (c) What is the probability that X exceeds its mean value? (Round your answer to four decimal places.) Why is this probability not 0.5? Since the lognormal distribution --Select-- v a symmetric distribution, the mean and the median of X --Select--- v…Nonpoint source loads are chemical masses that travel to the main stem of a river and its tributaries in flows that are distributed over relatively long stream reaches, in contrast to those that enter at well-defined and regulated points. An article suggests that for a certain time period and location, X nonpoint source load of total dissolved solids could be modeled with a lognormal distribution having mean value 10,647 kg/day/km and a coefficient of variation CV = 0.40 (CV = ох MX = USE SALT (a) What are the mean value and standard deviation of In(X)? (Round your answers to four decimal places.) mean value standard deviation (b) What is the probability that X is at most 15,000 kg/day/km? (Round your answer to four decimal places.) (c) What is the probability that X exceeds its mean value? (Round your answer to four decimal places.) Why is this probability not 0.5? Since the lognormal distribution is not ✓a symmetric distribution, the mean and the median of X are not ✓the same and, in…
- For a life aged 35, you are given a force of interest, 6=0.10, and a force of mortality, a= 0.06. This life purchases a ten-year deferred whole life insurance with a benefit of one payable at the moment of death. Z is the present value at poliey issue of the benefit for this insurance. Determine the 90th percentile of Z .choose the correct statement for the first order stationary random process X(ts): O a the PDF function change with time O b. the mean is function of time O. The variance is constant O d. The first order stationary random process is second order stationary random processThe lifetime X (in hundreds of hours) of a certain type of battery has a Weibull Distribution with parameters α =2 and β = 6. Compute the battery has at least 22 hours of lifetime.
- Assume δ = 0.05, ̄Ax = 0.06, 2 ̄Ax = 0.0040. A group of 100 lives age x purchasefully continuous whole life policies of face value $1,000 for continuous premiums of $3.50per year. Let L be the aggregate loss function (L =100∑i=1Li, where Li represents the netfuture loss of individual i). Calculate the mean and variance of the aggregate loss L.The average weight of a Coastal male Grizzly Bear is approximately normal with E(x); =795 pounds and SD * (x) = 80 pounds. 8. How likely is it to randomly select 64 Coastal male Grizzly Bears with a sample average weight of 810 pounds or more? Which density curve is the best model for this problem?a. What is the probability that the lifetime X of the first component exceeds 3? b. What are the marginal pdf's of X and Y? Are the two lifetimes independent? x. What is the probability that the lifetime of at least one component exceeds 3?
- Suppose a population of devices has a Weibull life distribution with β= 1.6 and θ= 25. What is the mean of the residual life distribution for copies of the device that survive 15 hours?A Gaussian random variable with variance 10 and mean 5 is transformed to Y=e. Find the pdf of Y.Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the variance of Y.