Suppose that a random sample of size 36, Y1,Y2,...,Y36, is drawn from a uniform pdf de...
Suppose that a random sample of size 36, Y1,Y2,...,Y36, is drawn from a uniform pdf de ned over the interval (0, θ), where θ is unknown. Set up a large- sample sign test for deciding whether or not the 25th per- centile of the Y -distribution is equal to 6. Let α = 0.05. With what probability will your procedure commit a Type II error if 7 is the true 25th percentile?
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large sample normality is used
to find type ii error probability. For further query in above,
comment.
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Suppose that a random sample of size 36, Y1,Y2,...,Y36, is drawn
from a uniform pdf de...
14.2.10. Suppose that a random sample of size 36, Y, Y2, ..., Y36, is drawn from...
14.2.10. Suppose that a random sample of size 36, Y, Y2, ..., Y36, is drawn from a uniform pdf defined over the interval (0, 0), where 0 is unknown. 'Set up a large- sample sign test for deciding whether or not the 25th percentile of the Y-distribution is equal to 6. Let a =0.05. With what probability will your procedure commit a Type II error if 7 is the true 25th percentile?
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be...
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be based on Xmax, the largest order statistic. What would be the probability of committing a Type II error when θ 1.7.
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS...
Let Y1 , Y2 , . . . , Yn denote a random sample from the...
Let Y1 , Y2 , . . . , Yn denote a random sample from the uniform
distribution on the interval (θ, θ+1). Let
a. Show that both ? ̂1 and ? ̂2 are unbiased estimators of
θ.
5. Let Yi,Y2, , Yn be a random sample of size n from the pdf (a)...
5. Let Yi,Y2, , Yn be a random sample of size n from the pdf (a) Show that θ = y is an unbiased estimator for θ (b) Show that θ = 1Y is a minimum-variance estimator for θ.
QUESTION 3 Let Y1, Y2, ..., Yn denote a random sample of size n from a...
QUESTION 3 Let Y1, Y2, ..., Yn denote a random sample of size n from a population whose density is given by (Parcto distribution). Consider the estimator β-Yu)-min(n, Y, where β is unknown (a) Derive the bias of the estimator β. (b) Derive the mean square error of B. , Yn).
2. [x] Suppose that Y1, Y2, Y3 denote a random sample from an exponential distribution whose...
2. [x] Suppose that Y1, Y2, Y3 denote a random sample from an exponential distribution whose pdf and cdf are given by f(y) = (1/0)e¬y/® and F(y) =1 – e-y/0, 0 > 0. It is also known that E[Y;] = 0. ', y > 0, respectively, with some unknown (a) Let X = min{Y1,Y2, Y3}. Show that X has pdf given by f(æ) = (3/0)e-3y/º. Start by thinking about 1- F(x) = Pr(min{Y1,Y2, Y3} > x) = Pr(Y1 > x,...
Let Y1, Y2, ..., Yn denote a random sample from an exponential distribution with mean θ
Let Y1, Y2, ..., Yn denote a random sample from an exponential distribution with mean θ. Find the rejection region for the likelihood ratio test of H0 : θ = 2 versus Ha : θ ≠ 2 with α = 0.09 and n = 14. Rejection region =
. Suppose the Y1, Y2, · · · , Yn denote a random sample from a...
. Suppose the Y1, Y2, · · · , Yn denote a random sample from a
population with Rayleigh distribution (Weibull distribution with
parameters 2, θ) with density function f(y|θ) = 2y θ e −y 2/θ, θ
> 0, y > 0
Consider the estimators ˆθ1 = Y(1) = min{Y1, Y2, · · · , Yn},
and ˆθ2 = 1 n Xn i=1 Y 2 i .
ii) (10 points) Determine if ˆθ1 and ˆθ2 are unbiased
estimators, and in...
Suppose X is Discrete Uniform(N). N is unknown. Thus, the pdf of X is given by f, (x:N)-N , N ; w...
Suppose X is Discrete Uniform(N). N is unknown. Thus, the pdf of X is given by f, (x:N)-N , N ; where N-|, 2,3, x# 1,2, We wish to test the hypotheses: H,: N 30 versus H,: N <30. Our critical region is of the form R-x: x <k. where k is an integer Find the largest value of k such that the test is level α 0.05. a) b) Using this k, what is the chance of type II...
Suppose X is Discrete Uniform(N). N is unknown. Thus, the pdf of X is given by f, (x:N) X1,2.. N;...
Suppose X is Discrete Uniform(N). N is unknown. Thus, the pdf of X is given by f, (x:N) X1,2.. N; where N 1,2,.3,.. We wish to test the hypotheses: H,: N- 30 versus H,: N <30. Our critical region is of the form R {x : x < k} , where k is an integer. Find the largest value of k such that the test is level α 0.05. a) β (10) Using this k, what is the chance of...
14.2.10. Suppose that a random sample of size 36, Y, Y2, ..., Y36, is drawn from a uniform pdf defined over the interval (0, 0), where 0 is unknown. 'Set up a large- sample sign test for deciding whether or not the 25th percentile of the Y-distribution is equal to 6. Let a =0.05. With what probability will your procedure commit a Type II error if 7 is the true 25th percentile?
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be based on Xmax, the largest order statistic. What would be the probability of committing a Type II error when θ 1.7.
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS...
Let Y1 , Y2 , . . . , Yn denote a random sample from the uniform
distribution on the interval (θ, θ+1). Let
a. Show that both ? ̂1 and ? ̂2 are unbiased estimators of
θ.
5. Let Yi,Y2, , Yn be a random sample of size n from the pdf (a) Show that θ = y is an unbiased estimator for θ (b) Show that θ = 1Y is a minimum-variance estimator for θ.
QUESTION 3 Let Y1, Y2, ..., Yn denote a random sample of size n from a population whose density is given by (Parcto distribution). Consider the estimator β-Yu)-min(n, Y, where β is unknown (a) Derive the bias of the estimator β. (b) Derive the mean square error of B. , Yn).
2. [x] Suppose that Y1, Y2, Y3 denote a random sample from an exponential distribution whose pdf and cdf are given by f(y) = (1/0)e¬y/® and F(y) =1 – e-y/0, 0 > 0. It is also known that E[Y;] = 0. ', y > 0, respectively, with some unknown (a) Let X = min{Y1,Y2, Y3}. Show that X has pdf given by f(æ) = (3/0)e-3y/º. Start by thinking about 1- F(x) = Pr(min{Y1,Y2, Y3} > x) = Pr(Y1 > x,...
. Suppose the Y1, Y2, · · · , Yn denote a random sample from a
population with Rayleigh distribution (Weibull distribution with
parameters 2, θ) with density function f(y|θ) = 2y θ e −y 2/θ, θ
> 0, y > 0
Consider the estimators ˆθ1 = Y(1) = min{Y1, Y2, · · · , Yn},
and ˆθ2 = 1 n Xn i=1 Y 2 i .
ii) (10 points) Determine if ˆθ1 and ˆθ2 are unbiased
estimators, and in...
Suppose X is Discrete Uniform(N). N is unknown. Thus, the pdf of X is given by f, (x:N)-N , N ; where N-|, 2,3, x# 1,2, We wish to test the hypotheses: H,: N 30 versus H,: N <30. Our critical region is of the form R-x: x <k. where k is an integer Find the largest value of k such that the test is level α 0.05. a) b) Using this k, what is the chance of type II...
Suppose X is Discrete Uniform(N). N is unknown. Thus, the pdf of X is given by f, (x:N) X1,2.. N; where N 1,2,.3,.. We wish to test the hypotheses: H,: N- 30 versus H,: N <30. Our critical region is of the form R {x : x < k} , where k is an integer. Find the largest value of k such that the test is level α 0.05. a) β (10) Using this k, what is the chance of...
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