Homework Answers
I have used central limit theorem as the sample size is 40 and
when the sample size is above 30,we will use central limit theorem
as the random samples are independent and identically distributed
random variables with mean 
and finite variance 
.Then the solution should be:
![XuXg.....X40 fx (2) where fx (x) = 532² 0<x< 1 2 o .o.w. PC 2X: 72-8] - ? Let Sn= I xi Here, the sample size is 40 Then, we c](http://img.homeworklib.com/questions/573cf3b0-6f6b-11ea-b75c-e1ae9738960a.png?x-oss-process=image/resize,w_560)
![Now, P[Sn 32.8] - 1-P [Son 52.8] 2 1 - P[Sn- 3 2 2.8-3] 2 1 - PT VAO (S n-3/) < $40 (2.05) e I - PJ V40 (Sn-3)< 12.96] - 1-P](http://img.homeworklib.com/questions/57c81110-6f6b-11ea-92b7-337931768a1c.png?x-oss-process=image/resize,w_560)
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12. Suppose that X1, X2, ,X40 denote a random sample of measurements on the proportion of...
Suppose that X. X. .... Xso denote a random sample of measurements on the proportion of...
Suppose that X. X. .... Xso denote a random sample of measurements on the proportion of impurities in iron ore samples. Let each variable X, have a probability density function given by fx/X) = 3x2 0<x< 1. The ore is to be rejected by the potential buyer if X1 + X2+...+X40 exceeds 2.8. Let X = X1 + X2 + ....+X40. Find Var). Answer:
by central limit theorem 12. Suppose that X1, X2, ..., X 40 denote a random sample...
by
central limit theorem
12. Suppose that X1, X2, ..., X 40 denote a random sample of measurements on the proportion of impurities in iron ore samples. Let each variable X have a probability density function given by 132 0<x<1 o elsewhere The ore is to be rejected by the potential buyer if sample of size 40 X, exceeds 2.8. Estimate P ., X. > 2.8) for the
Assume that X1, X2, . . . , Xn denote a random sample from a population...
Assume that X1, X2, . . . , Xn denote a random sample from a population with the following probability density function : fX(x|α) = αβ / (α + βx)^2 , x > 0 where α > 0 and β > 0. find the limiting distribution of nβX(1).
Let X1, X2, ..., Xn denote a random sample of size n from a population whose...
Let X1, X2, ..., Xn denote a random sample of size n from a population whose density fucntion is given by 383x-4 f S x f(x) = 0 elsewhere where ß > 0 is unknown. Consider the estimator ß = min(X1, X2, ...,Xn). Derive the bias of the estimator ß.
Let X1,X2,...,Xn denote a random sample from the Rayleigh distribution given by f(x) = ...
Let X1,X2,...,Xn denote a random sample from the Rayleigh distribution given by f(x) = (2x θ)e−x2 θ x > 0; 0, elsewhere with unknown parameter θ > 0. (A) Find the maximum likelihood estimator ˆ θ of θ. (B) If we observer the values x1 = 0.5, x2 = 1.3, and x3 = 1.7, find the maximum likelihood estimate of θ.
need solution 1. [5 marks] The proportion of lost packets Types I and II in a network are random variables X1 and X2...
need solution
1. [5 marks] The proportion of lost packets Types I and II in a network are random variables X1 and X2 with the joint probability density function J+2 for 0a1S1,0s1 fx,X, (1,) elsewhere. What is the covariance between these two proportions? Solution: The covariance betweon these two pronorti
Let X1, X2, ..., Xn be a random sample of size n from a population that...
Let X1, X2, ..., Xn be a random sample of size n from a population that can be modeled by the following probability model: axa-1 fx(x) = 0 < x < 0, a > 0 θα a) Find the probability density function of X(n) max(X1,X2, ...,Xn). b) Is X(n) an unbiased estimator for e? If not, suggest a function of X(n) that is an unbiased estimator for e.
Let X1, X2, ...,Xn be a random sample of size n from a population that can...
Let X1, X2, ...,Xn be a random sample of size n from a population that can be modeled by the following probability model: axa-1 fx(x) = 0 < x < 0, a > 0 θα a) Find the probability density function of X(n) = max(X1, X2, ...,xn). b) Is X(n) an unbiased estimator for e? If not, suggest a function of X(n) that is an unbiased estimator for 0.
8. Let X1,...,Xn denote a random sample of size n from an exponential distribution with density function given by, 1 -x...
8. Let X1,...,Xn denote a random sample of size n from an exponential distribution with density function given by, 1 -x/0 -e fx(x) MSE(1). Hint: What is the (a) Show that distribution of Y/1)? nY1 is an unbiased estimator for 0 and find (b) Show that 02 = Yn is an unbiased estimator for 0 and find MSE(O2). (c) Find the efficiency of 01 relative to 02. Which estimate is "better" (i.e. more efficient)?
8. Let X1,...,Xn denote a random...
Let (X1, Y1) and (X2, Y2) be independent and identically distributed continuous bivariate random variables with joint pr...
Let (X1, Y1) and (X2, Y2) be independent and identically distributed continuous bivariate random variables with joint probability density function: fX,Y (x,y) = e-y, 0 <x<y< ; =0 , elsewhere. Evaluate P( X2>X1, Y2>Y1) + P (X2 <X1, Y2<Y1) .
Suppose that X. X. .... Xso denote a random sample of measurements on the proportion of impurities in iron ore samples. Let each variable X, have a probability density function given by fx/X) = 3x2 0<x< 1. The ore is to be rejected by the potential buyer if X1 + X2+...+X40 exceeds 2.8. Let X = X1 + X2 + ....+X40. Find Var). Answer:
by
central limit theorem
12. Suppose that X1, X2, ..., X 40 denote a random sample of measurements on the proportion of impurities in iron ore samples. Let each variable X have a probability density function given by 132 0<x<1 o elsewhere The ore is to be rejected by the potential buyer if sample of size 40 X, exceeds 2.8. Estimate P ., X. > 2.8) for the
Let X1, X2, ..., Xn denote a random sample of size n from a population whose density fucntion is given by 383x-4 f S x f(x) = 0 elsewhere where ß > 0 is unknown. Consider the estimator ß = min(X1, X2, ...,Xn). Derive the bias of the estimator ß.
need solution
1. [5 marks] The proportion of lost packets Types I and II in a network are random variables X1 and X2 with the joint probability density function J+2 for 0a1S1,0s1 fx,X, (1,) elsewhere. What is the covariance between these two proportions? Solution: The covariance betweon these two pronorti
Let X1, X2, ..., Xn be a random sample of size n from a population that can be modeled by the following probability model: axa-1 fx(x) = 0 < x < 0, a > 0 θα a) Find the probability density function of X(n) max(X1,X2, ...,Xn). b) Is X(n) an unbiased estimator for e? If not, suggest a function of X(n) that is an unbiased estimator for e.
Let X1, X2, ...,Xn be a random sample of size n from a population that can be modeled by the following probability model: axa-1 fx(x) = 0 < x < 0, a > 0 θα a) Find the probability density function of X(n) = max(X1, X2, ...,xn). b) Is X(n) an unbiased estimator for e? If not, suggest a function of X(n) that is an unbiased estimator for 0.
8. Let X1,...,Xn denote a random sample of size n from an exponential distribution with density function given by, 1 -x/0 -e fx(x) MSE(1). Hint: What is the (a) Show that distribution of Y/1)? nY1 is an unbiased estimator for 0 and find (b) Show that 02 = Yn is an unbiased estimator for 0 and find MSE(O2). (c) Find the efficiency of 01 relative to 02. Which estimate is "better" (i.e. more efficient)?
8. Let X1,...,Xn denote a random...
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