14.Show that for the Gamma distributionedp =dx, 0

Answered: Image /qna-images/answer/f469e41d-d134-4339-af35-2387a345508d.jpg

Answered: Show that for the Gamma distribution…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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D5) Consider the logistic regression model P(Y=1) = 1 /( 1 + exp(-(a+bx))) where a = 1, b = 1.5 and the errors are normally distributed with mean 0 and standard deviation 1. Let x be a sequence from -4 to 4 in increments of 0.1. Estimate the bias of the slope for a simple linear regression model at x = 0 compared to the true slope (change in probability over change in x) of the logistic function at x = 0
2. How is the exponential distribution related to each of the following? (a) Gamma (b) Chi square Weibull. (c)
if it was XN(6) Between that - the Mean deviation in this distribution is 2 6 T the First Spring is Q-μ- 0.676 And the third Spring is or μ+ 0.676
(d) At any time, find the mean age of insects in the population. (e) Sketch g(x), the p.d.f. of the age distribution of insects in the population. (f) No calculations are required for this part of the question.Now suppose that a population with the life table function Q(x) thatyou obtained in part (b) is stable but not stationary. Describe brieflyhow the age distribution of the population would differ from that of astationary population with the same life table function if the populationis (i) growing, (ii) declining. Draw rough sketches to show what thep.d.f. of the age distribution might look like in each case.
Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken 8 blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.85mg/dl.(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (b) What conditions are necessary for your calculations? (c) interpret your results in the context of this problem. (d)Sample size find the sample size necessary for a 95% confidence level maximal margin of error E=1.10 for the mean concentration of uric acid in this patient's blood.
Find the method of moments estimator for the parameters of the double exponential distribution DE(0,n) f(x) Le-lz-nl/, - 0 0. 20
Calculate the mean and the standard deviation of the normal variable X from the following data. P(X < 95) = 0.09, P(X < 105) = 0.97 Let X ~ N (μ , σ²)
The height of an object t seconds after it is dropped from a height of 140 meters is s(t) = -4.9t² + 140. (a) Find the average velocity of the object during the first 5 seconds. m/s (b) Use the Mean Value Theorem to verify that at some time during the first 5 seconds of fall, the instantaneous velocity equals the average velocity. Find that time. S
5. S Jn Show that the 95 percent fiducial limits for the mean of the population are x ± to.05, where to.05, stands for the value of t at 5 percent level of significance. Deduce that for a random sample of 16 values with mean 41.5 inches and the sum of the squares of the deviations from the mean 135 (inches)² and drawn from a normal population, 95 percent fiducial limits for the mean of the population are 39.9 and 43-1 inches.
Let Y be a random variable with the mgfM(t) = .35e^(−4t) + .1 + .25e^(2t) + .3e^(4t).(a) What is the pmf of Y?(b) Calculate the variance of Y directly from the pmf you determined in part (a).(c) Calculate E[Y^4] directly from the mgf.
t x, x, ... x be a random sample from an exponential distribution with parameter 0. Find sufficient estimator for '8'.

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Show that for the Gamma distribution e*x dp = 14. dx, 0