QUESTION 1Let X1, X2, X3, X4 be the lifetimes (in hours) of a random sample of 4 light bulbs. Futhermore,suppose that the lifetime of each bulb has a distribution with probability density function1expif 0 < a < x < 0 and ß > 0,Bf(x|a, ß) =otherwise;and moment generating function M(t) =1– Bteattß < 1.If the observations are 820, 910, 1060, and 490, what are:(a) the method of moments estimates of a and ß; and(b) the maximum likelihood estimates of a and ß?

Please find step by step below. the answer is given using moment and likelihood.

QUESTION 1 Let X1, X2, X3, X4 be the lifetimes (in hours) of a random sample of 4 light bulbs. Futhermore, suppose that the lifetime of each bulb has a distribution with probability density function 1 exp B if o < a sx < o∞o and ß > 0, S(x|a, ß) = otherwise; and moment generating function M(t) : tß < 1. 1– Bt If the observations are 820, 910, 1060, and 490, what are: (a) the method of moments estimates of a and ß; and (b) the maximum likelihood estimates of a and 8?

QUESTION 1 Let X1, X2, X3, X4 be the lifetimes (in hours) of a random sample of 4 light bulbs. Futhermore, suppose that the lifetime of each bulb has a distribution with probability density function 1 exp B if o < a sx < o∞o and ß > 0, S(x|a, ß) = otherwise; and moment generating function M(t) : tß < 1. 1– Bt If the observations are 820, 910, 1060, and 490, what are: (a) the method of moments estimates of a and ß; and (b) the maximum likelihood estimates of a and 8?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

1 The time between major earthquakes in the Taiwan region is a random variable with probability density function f(t) = -t/3650.1 where t is measured in days. 3650.1 A. Find the probability that the time between a major earthquake and the next one is more than 2 years but less than 6 years. B. Find the probability that the time between a major earthquake and the next one is more than 8030 days.
Let X1, X2, ..., Xn be a random sample from a population with probability density function 4 - 33 √T.² Find a sufficient statistic for 3. Justify your answer. f(x) = 0 < x <∞.
Suppose Y · Uniform(01,02) where the parameters and O2 take the values -1 and 2 respectively. Compute the probability P(Y < y) when y=1.41.
Q.3 The probability density function for a continuous random variable X is fx (x) = {"* Sa+ bx2; 0< x< 1, 0; %3D е. w. (i) Find constants a and b if E(X) = 0.6 (ii) Find cumulative distribution function (cdf), moment generating function. (iii) Using mgf, find B1 and Bß2 and comment on it. (iv) Sketch pdf and cdf.
Suppose a fair coin is tossed 3 times. Define the r.v.'s X = number of Heads and Y = 1(0) if H (T) occurs on the first toss. Find the joint probability function for (X, Y).
4. The lifetime in hours of an electronic gadget is a random variable having a probability density function of x2 0. Compute the expected lifetime of such a gadget. f(x) = xe-2x
two random independant variables X and Y with distributions: X ∼ Poisson(λ) og Y ∼ Poisson(2λ), andobservations x = 2 og y = 5 .(a) What is the log-likelihood function? b) calculate MLE for the observated samples
Suppose that X is a random variable having the following probability density function given by (2(0-x) x>0 f(x) = elsewhere Find the value of c such that an interval from x to cx is a (1-a)100% confidence interval for the parameter 8.
Suppose that a random variable X has the following probability density function. SC (64-x²) 0 ≤ x ≤ 8 otherwise f(x) = {C Find the expected value of X. (You will need to find the value of the constant C so that f is a pdf.)
and variance of X if the probability mass function is f(x) = ; ;)" , Find the moment generating function, mean x = 1, 2, 3, 4, ...
do part b,c,d
Suppose Y - Uniform(01, 02) where the parameters and 02 take the values 1 and 5 respectively. Compute the probability P(Y < y) when y=4.71.