The number X of typographic mistakes in a book about Machine Learning is a random variable Po(λ). Based in his experience, an editor supposes that λ ∼ Gamma(α,β).
a) Obtain the final distribution of λ | X
b) Determine the predictive final distribution of a new mistake.
The number X of typographic mistakes in a book about Machine Learning is a random variable...
9. (9 pts) The random variable r-Gamma(x-2, β-4). functions to prove that the moment generating function for the random variable W mw(t) (1-12t)2. Use the method of moment-generating 3Y +5is eSt 10, (9 pts) Suppose that Y has a gamma distribution with α-n/2 for some positive integer n and β equal to some specified value. Use the method of moment-generating functions to prove that W- 2Y /g has a Chi-squared distribution with n degrees of freedom. Make sure you show...
Random variable X corresponds to the daily number of accidents in a small town during the first week of January. From the previous experience (prior infor- mation), local police Chief Smith tends to believe that the mean daily number of accidents is 2 and the variance is also 2. We also observe for the current year the sample number of accidents for 5 days in a row: 5,2,1,3,3. Let us assume that X has Poisson distribution with parameter θ ....
solve the following questions- 1. Suppose that a random variable X follows gamma distribution with shape parameter α and scale β. Determine the values of α and β given that E(X) = 8 and Var(X) = 32. 2. A commonly used practice of airline companies is to sell more tickets than actual seats to a particular flight because customers who buy tickets do not always show up for the flight. Suppose that the percentage of no shows at flight time...
1. Let the random variable X represent the number of defective parts for a machine when 3 parts are sampled from a production line and tested. The following is the probability distribution of X 0 1 T0.38 2 3 х 0.10 0.01 0.51 (a) Compute expected value of the random variable X c) ) S 0. the l (b) Compute standard deviation of the random variable X (c) If g(X) = 2X +3, what is the expected value of g(X)?...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.7 with sample standard deviation s = 3.4. Use a...
1.) In the previous question (the one about the multiple-choice quiz), the random variable X is binomial with parameters: n = 1/5, p = 15 n = 15, p = 1/2 n = 15, p = 1/5 n = 15, p = 0 2.) Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use technology to find the probability distribution given the probability p=0.164p=0.164 of success on a single trial. (Report answers accurate to 4...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Thenx has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows.16181719141314171610(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your...
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.78. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9...
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.66. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9...