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(b) For n = 100, give an approximaation for P(Y> 100) (c) Let X be the...
Dr. Beldi Qiang STATWOB Flotllework #1 1. Let X.,No X~ be a i.İ.d sample form Exp(1),...
Dr. Beldi Qiang STATWOB Flotllework #1 1. Let X.,No X~ be a i.İ.d sample form Exp(1), and Y-Σ-x. (a) Use CLT to get a large sample distribution of Y (b) For n 100, give an approximation for P(Y> 100) (c) Let X be the sample mean, then approximate P(.IX <1.2) for n 100. x, from CDF F(r)-1-1/z for 1 e li,00) and ,ero 2Consider a random sample Xi.x, 、 otherwise. (a) Find the limiting distribution of Xim the smallest order...
3. Suppose that X1,X2, ,Xn are i.id. N(0, σ2). Find a function of T(X)-Σǐii verges in...
3. Suppose that X1,X2, ,Xn are i.id. N(0, σ2). Find a function of T(X)-Σǐii verges in distribution to a normal distribution. State the mean and variance of your limiung normal distribution. 4. Stirling's Formula, which gives approximation for factorials, can be derived using CLT. (a) Suppose that X1, X2, random variable Z, .Xn is an ii.d. sample from Exp(1). Show that, for a standard normal PTPZ) (b) Show by differencing both sides of the approximation in part a. Then set...
(a) Suppose that i, X2,... , In is an i.i.d. sample from Exp(1). Show that, for...
(a) Suppose that i, X2,... , In is an i.i.d. sample from Exp(1). Show that, for a standard normal random variable Z b) Show Г(n) by differencing both sides of the approximation in part a. Then set a -0 to get Stirling's Formula. 5. Suppose that Y is an id sample from Negative Binomial (n,p). Give a normal approximation of Yn use CLT, when n is large. 6. (Mandatory for Graduate Student. Extra credit for undergrad.) Let Ai, converges to...
tirling's Formula, which gives approximation for factorials, can be derived using CLT. (a) Suppose that X1,...
tirling's Formula, which gives approximation for factorials, can be derived using CLT. (a) Suppose that X1, X2, random variable Z, , Xn is an ii.d. sample from Exp(1). Show that, for a standard normal (b) Show by differencing both sides of the approximation in part a. Then set 0 to get Stirling's Formula.
Stirling’s Formula, which gives approximation for factorials, can be derived using CLT. (a) Suppose that X1,...
Stirling’s Formula, which gives approximation for factorials, can be derived using CLT. (a) Suppose that X1, X2, · · · , Xn is an i.i.d. sample from Exp(1). Show that, for a standard normal random variable Z, (b) Show by differencing both sides of the approximation in part a. Then set x = 0 to get Stirling’s Formula. We were unable to transcribe this imageГ(n) уж
1. Let Xi, X2, X, be a 1.1.d. sample form Exp(1), and Y = Σ=i Xi....
1. Let Xi, X2, X, be a 1.1.d. sample form Exp(1), and Y = Σ=i Xi. (a) Use CLT to get a large sample distribution of Y (b) For n = 100, give an approximation for P(Y > 100) (c) Let X be the sample mean, then approximate P(1.1 < X < 1.2) for n = 100.
l Exam.(Jan 15) Circle out your Class Mon& Wed or Mon.Evening 3) Suppose X,x,X, (n>1) is...
l Exam.(Jan 15) Circle out your Class Mon& Wed or Mon.Evening 3) Suppose X,x,X, (n>1) is a random sample from Bernoulli distribution with p.mf. p(x)-p"(1-p)'",x= 0,1, , then follows ( ). BBinomial distribution B(n.p) D can not be determined. A Normal distribution N(np,np(1-p) Poisson distribution P(np)
Let X1 , . . . , xn be n iid. random variables with distribution N (θ, θ) for some unknown θ > 0....
Let X1 , . . . , xn be n iid. random variables with distribution N (θ, θ) for some unknown θ > 0. In the last homework, you have computed the maximum likelihood estimator θ for θ in terms of the sample averages of the linear and quadratic means, i.e. Xn and X,and applied the CLT and delta method to find its asymptotic variance. In this problem, you will compute the asymptotic variance of θ via the Fisher Information....
5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show th...
1.(c)
2.(a),(b)
5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show that the UMVUE of θ 2 is X2-1/n x"-'e-x/θ , x > 0.0 > 0 6. Let Xi, ,Xn be i.i.d. gamma(α,6) where α > l is known. ( f(x) Γ(α)θα (a) Show that Σ X, is complete and sufficient for θ (b) Find ElI/X] (c) Find the UMVUE of 1/0 -e λ , X > 0 2) (x...
3. (20 marks) Suppose Y...Y is a random sample of independent and identically distributed Gamma(c...
3. (20 marks) Suppose Y...Y is a random sample of independent and identically distributed Gamma(c, B) random variables. Suppose c is a known constant. a) (5 marks) Find an exact (I-a)100% CI. forty: cß based on Y. Hint: Make use of the Chi-Square distribution when finding your pivot. b) (5 marks) Find an approximate (1-α)100% CI. forMy-cß based on only Y using a n (Y-CB) ~ Normal (0, Normal approximation and the pivot Z- c) (5 marks) Find an approximate...
Dr. Beldi Qiang STATWOB Flotllework #1 1. Let X.,No X~ be a i.İ.d sample form Exp(1), and Y-Σ-x. (a) Use CLT to get a large sample distribution of Y (b) For n 100, give an approximation for P(Y> 100) (c) Let X be the sample mean, then approximate P(.IX <1.2) for n 100. x, from CDF F(r)-1-1/z for 1 e li,00) and ,ero 2Consider a random sample Xi.x, 、 otherwise. (a) Find the limiting distribution of Xim the smallest order...
3. Suppose that X1,X2, ,Xn are i.id. N(0, σ2). Find a function of T(X)-Σǐii verges in distribution to a normal distribution. State the mean and variance of your limiung normal distribution. 4. Stirling's Formula, which gives approximation for factorials, can be derived using CLT. (a) Suppose that X1, X2, random variable Z, .Xn is an ii.d. sample from Exp(1). Show that, for a standard normal PTPZ) (b) Show by differencing both sides of the approximation in part a. Then set...
(a) Suppose that i, X2,... , In is an i.i.d. sample from Exp(1). Show that, for a standard normal random variable Z b) Show Г(n) by differencing both sides of the approximation in part a. Then set a -0 to get Stirling's Formula. 5. Suppose that Y is an id sample from Negative Binomial (n,p). Give a normal approximation of Yn use CLT, when n is large. 6. (Mandatory for Graduate Student. Extra credit for undergrad.) Let Ai, converges to...
tirling's Formula, which gives approximation for factorials, can be derived using CLT. (a) Suppose that X1, X2, random variable Z, , Xn is an ii.d. sample from Exp(1). Show that, for a standard normal (b) Show by differencing both sides of the approximation in part a. Then set 0 to get Stirling's Formula.
1. Let Xi, X2, X, be a 1.1.d. sample form Exp(1), and Y = Σ=i Xi. (a) Use CLT to get a large sample distribution of Y (b) For n = 100, give an approximation for P(Y > 100) (c) Let X be the sample mean, then approximate P(1.1 < X < 1.2) for n = 100.
l Exam.(Jan 15) Circle out your Class Mon& Wed or Mon.Evening 3) Suppose X,x,X, (n>1) is a random sample from Bernoulli distribution with p.mf. p(x)-p"(1-p)'",x= 0,1, , then follows ( ). BBinomial distribution B(n.p) D can not be determined. A Normal distribution N(np,np(1-p) Poisson distribution P(np)
Let X1 , . . . , xn be n iid. random variables with distribution N (θ, θ) for some unknown θ > 0. In the last homework, you have computed the maximum likelihood estimator θ for θ in terms of the sample averages of the linear and quadratic means, i.e. Xn and X,and applied the CLT and delta method to find its asymptotic variance. In this problem, you will compute the asymptotic variance of θ via the Fisher Information....
1.(c)
2.(a),(b)
5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show that the UMVUE of θ 2 is X2-1/n x"-'e-x/θ , x > 0.0 > 0 6. Let Xi, ,Xn be i.i.d. gamma(α,6) where α > l is known. ( f(x) Γ(α)θα (a) Show that Σ X, is complete and sufficient for θ (b) Find ElI/X] (c) Find the UMVUE of 1/0 -e λ , X > 0 2) (x...
3. (20 marks) Suppose Y...Y is a random sample of independent and identically distributed Gamma(c, B) random variables. Suppose c is a known constant. a) (5 marks) Find an exact (I-a)100% CI. forty: cß based on Y. Hint: Make use of the Chi-Square distribution when finding your pivot. b) (5 marks) Find an approximate (1-α)100% CI. forMy-cß based on only Y using a n (Y-CB) ~ Normal (0, Normal approximation and the pivot Z- c) (5 marks) Find an approximate...
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