Homework Answers
Add Answer to:
(Mathematical Statistics)
Problem 1. (a) Formulate and prove Basu's Theorem. Do not forget to give definitions...
Problem 3 Let X1, X2, ... , Xn be a random sample of size n from...
Problem 3 Let X1, X2, ... , Xn be a random sample of size n from a Gamma distribution fr; a,B) 22-12-1/B, 0 < < (a) Find a sufficient statistics for a. (b) Find a sufficient statistics for B.
Problem 1 (20 points). Suppose X1, X2, ... , Xn are a random sample from the...
Problem 1 (20 points). Suppose X1, X2, ... , Xn are a random sample from the uniform distribution over [0, 1]. (i) Let In be the sample mean, derive the Central Limit Theorem for år. (ii) Calculate E(X) and Var(x}). (iii) Let Yn = (1/n) - X. Derive the Central Limit Theorem for Yn. (iv) Set Zn = 1/Yn. Derive the Central Limit Theorem for Zn.
Formulate the following problems as least-squares problems. For each problem, give a matrix A and a vector b, such that the problem can be expressed as minimize IAx-bi (You do not have to solve the p...
Formulate the following problems as least-squares problems. For each problem, give a matrix A and a vector b, such that the problem can be expressed as minimize IAx-bi (You do not have to solve the problems.) (a) Minimize x1+ 2x + 3x[+ (x,-x2 + x3-1)2 + (-ri-4x2 + 2)2. (b) Minimize (-6r2 4)43r228r2-3)2 (e) Minimize 2(-6x2+ 4)2 + 3(-4x1 +3x2-1尸+4(x1 + 8x2-3)2. 1+(-i - 4r2 +2)2
Formulate the following problems as least-squares problems. For each problem, give a matrix A...
Probability & Statistics for Engineers & Scientists 9th edition 9.82 Consider the lognormal distribution with the...
Probability & Statistics for Engineers & Scientists 9th edition 9.82 Consider the lognormal distribution with the density function given in Section 6.9. Suppose we have a random sample x1,x2,....,xn from a lognormal distribution. (a) Write out the likelihood function. (b)Develop the maximum likelihood estimates of mean and variance of random variable.
L.11) Brand name distributions a) Give an example of a normally distributed random variable. b) Give...
L.11) Brand name distributions a) Give an example of a normally distributed random variable. b) Give an example of an exponentially distributed random variable. c) Give an example of a random variable with the Weibull distribution. d) Give an example of a random variable with the Pareto distribution. L.4) Sample means from BinomialDist[1, p] IfXl. X2. X3, Xn are independent random samples from a random variable with the BinomialDist[1, p] distribution, then what normal cumulative distribution function do you use...
(x-2) 5. a) Let S Prove that s? Po? n-1 b) Consider a sequence of random...
(x-2) 5. a) Let S Prove that s? Po? n-1 b) Consider a sequence of random variables {Xn} with pdf, fx, (x) = xht where 1<x<. Obtain Fx (2) and hence find the limiting distribution of X, as noo. c) Consider a random sample of size n from Fx (x) = where - <I<0. Find the limiting distribution of Yn as n + if (a)' = n max{X1, X2, X3,...,xn). and X(n) [17 marks]
Problem 7 a) Show that n 1 Xi and n 1 X? are jointly sufficient statistics for two un- known para...
Problem 7 a) Show that n 1 Xi and n 1 X? are jointly sufficient statistics for two un- known parameters of the normal distribution N(01, 02) (based on the data sample Xi,..., Xn) in two ways: by factorization theorem and using the property of the exponential family. c) Give yet another example of a couple of jointly sufficient statistics. solution into your homework (not just refer to the aforementi statistic, have you checked that this function is invertible? b)...
Prove the Binomial Theorem, that is Exercises 173 (vi) x+y y for all n e N...
Prove the Binomial Theorem, that is Exercises 173 (vi) x+y y for all n e N C) Recall that for all 0rS L is divisible by 8 when n is an odd natural number vii))Show that 2 (vin) Prove Leibniz's Theorem for repeated differentiation of a product: If ande are functions of x, then prove that d (uv) d + +Mat0 for all n e N, where u, and d'a d/v and dy da respectively denote (You will need to...
1. Give the experimental line a real test. Come up with an n so that if...
1. Give the experimental line a real test. Come up with an n so
that if the experimental line produces n chips with failure rate
6/38 or less, then the probability of getting a failure rate 6/38
or less under the original production system is less than 0.01.
2. If two random variables have the same generating function,
must they have the same cumulative distribution function?
L.9) Central Limit Theorem Central Limit Theorem Version 1 says Go with independent random...
Problem 3. Prove Theorem 1 as tollows [Assume all conditions of the Theorem are met. In many part...
Problem 3. Prove Theorem 1 as tollows [Assume all conditions of the Theorem are met. In many parts, it will be useful to consider the sign of the right side of the formula-positive or negative- ad to write the appropriate inequality] (a) Since f"(x) exists on [a, brx) is continuous on [a, b) and differentiable on (a,b), soMean Value Thorem applies to f,on this interval. Apply MVTtof"m[x,y], wherc α zcysb. to show that ry)2 f,(x), İ.e. that f, is increasing...
Problem 3 Let X1, X2, ... , Xn be a random sample of size n from a Gamma distribution fr; a,B) 22-12-1/B, 0 < < (a) Find a sufficient statistics for a. (b) Find a sufficient statistics for B.
Problem 1 (20 points). Suppose X1, X2, ... , Xn are a random sample from the uniform distribution over [0, 1]. (i) Let In be the sample mean, derive the Central Limit Theorem for år. (ii) Calculate E(X) and Var(x}). (iii) Let Yn = (1/n) - X. Derive the Central Limit Theorem for Yn. (iv) Set Zn = 1/Yn. Derive the Central Limit Theorem for Zn.
Formulate the following problems as least-squares problems. For each problem, give a matrix A and a vector b, such that the problem can be expressed as minimize IAx-bi (You do not have to solve the problems.) (a) Minimize x1+ 2x + 3x[+ (x,-x2 + x3-1)2 + (-ri-4x2 + 2)2. (b) Minimize (-6r2 4)43r228r2-3)2 (e) Minimize 2(-6x2+ 4)2 + 3(-4x1 +3x2-1尸+4(x1 + 8x2-3)2. 1+(-i - 4r2 +2)2
Formulate the following problems as least-squares problems. For each problem, give a matrix A...
L.11) Brand name distributions a) Give an example of a normally distributed random variable. b) Give an example of an exponentially distributed random variable. c) Give an example of a random variable with the Weibull distribution. d) Give an example of a random variable with the Pareto distribution. L.4) Sample means from BinomialDist[1, p] IfXl. X2. X3, Xn are independent random samples from a random variable with the BinomialDist[1, p] distribution, then what normal cumulative distribution function do you use...
(x-2) 5. a) Let S Prove that s? Po? n-1 b) Consider a sequence of random variables {Xn} with pdf, fx, (x) = xht where 1<x<. Obtain Fx (2) and hence find the limiting distribution of X, as noo. c) Consider a random sample of size n from Fx (x) = where - <I<0. Find the limiting distribution of Yn as n + if (a)' = n max{X1, X2, X3,...,xn). and X(n) [17 marks]
Problem 7 a) Show that n 1 Xi and n 1 X? are jointly sufficient statistics for two un- known parameters of the normal distribution N(01, 02) (based on the data sample Xi,..., Xn) in two ways: by factorization theorem and using the property of the exponential family. c) Give yet another example of a couple of jointly sufficient statistics. solution into your homework (not just refer to the aforementi statistic, have you checked that this function is invertible? b)...
Prove the Binomial Theorem, that is Exercises 173 (vi) x+y y for all n e N C) Recall that for all 0rS L is divisible by 8 when n is an odd natural number vii))Show that 2 (vin) Prove Leibniz's Theorem for repeated differentiation of a product: If ande are functions of x, then prove that d (uv) d + +Mat0 for all n e N, where u, and d'a d/v and dy da respectively denote (You will need to...
1. Give the experimental line a real test. Come up with an n so
that if the experimental line produces n chips with failure rate
6/38 or less, then the probability of getting a failure rate 6/38
or less under the original production system is less than 0.01.
2. If two random variables have the same generating function,
must they have the same cumulative distribution function?
L.9) Central Limit Theorem Central Limit Theorem Version 1 says Go with independent random...
Problem 3. Prove Theorem 1 as tollows [Assume all conditions of the Theorem are met. In many parts, it will be useful to consider the sign of the right side of the formula-positive or negative- ad to write the appropriate inequality] (a) Since f"(x) exists on [a, brx) is continuous on [a, b) and differentiable on (a,b), soMean Value Thorem applies to f,on this interval. Apply MVTtof"m[x,y], wherc α zcysb. to show that ry)2 f,(x), İ.e. that f, is increasing...
Most questions answered within 3 hours.
-
Consider the following reaction at equilibrium. What will happen
if O2 is added to the reaction?...
asked 4 minutes ago -
Based on how much or how little you have noticed in the media,
do you think...
asked 2 hours ago -
I calculate Rosetta Stone’s P/E ratio as 10x prior to a report
about future industry growth....
asked 3 hours ago -
What major physiological changes account for electrodermal
activity (as in during a lie-detector test)?
asked 4 hours ago -
You are going to sell fruits & vegetables at a local
roadside market. List separately and...
asked 5 hours ago -
Hows does water affect the digestion of fats ?
asked 7 hours ago -
A buffer that contains 0.41 M of a base, B and 0.21 M of its
conjugate...
asked 7 hours ago -
Pleaaaaaaaasssssse help me please please it's more important
:((((((((((((((((((((
CASE STUDY
Nissan Company
Nissan Motor Company,...
asked 7 hours ago -
Calculate the concentration of hydronium and hyroxide ions in 1)
2.0 mol/L HNO3 2) 0.5 mol/L...
asked 8 hours ago -
In a loop-the-loop ride a car goes around a vertical, circular
loop at a constant speed....
asked 8 hours ago -
50 grams each of water (18.015 g/mol) and ethylene glycol
(C2H6O2) (62.07 g/mol) are mixed. At...
asked 8 hours ago -
The life expectancy of sport utility vehicles follows a normal
distribution with a mean of 145.8...
asked 8 hours ago