Find the Neyman-Pearson most powerful test of its size Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake

Question

Question

Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake

Find the Neyman-Pearson most powerful test of its size

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

te 10 (97 のD)

Add a comment

Answer 2

Similar Homework Help Questions

3. Let Y be a random variable whose probability mass function under Ho and Hi is givern by 1 23 4 5 6 7 f(yHo) .01 01 01 01 01 01 94 fulHi) 06 0504 .03 02 01 79 Use the Neyman-Pearson Lemma to find...

3. Let Y be a random variable whose probability mass function under Ho and Hi is givern by 1 23 4 5 6 7 f(yHo) .01 01 01 01 01 01 94 fulHi) 06 0504 .03 02 01 79 Use the Neyman-Pearson Lemma to find the most powerful test for Ho versus Hi with Use the Nevmam-Pearson Lemma to find the mst size α-004. Compute the probability of a Type II error for this test. 3. Let Y be a...
please see picture 5. Let X1, X2,..., Xn be Bin(2,0) random variables with Θ {.45, .65). For testing Ho : θ 45 versus HA : θ-66, determine the following: (a) the form of the Neyman-Pearson MP crit...

please see picture 5. Let X1, X2,..., Xn be Bin(2,0) random variables with Θ {.45, .65). For testing Ho : θ 45 versus HA : θ-66, determine the following: (a) the form of the Neyman-Pearson MP critical region for a size a test (b) the sampling distribution of 2iI X (c) the value of ho for α A.05 when n-20. (d) π(8) for α .05 when n-20. a random sample of lid 5. Let X1, X2,..., Xn be Bin(2,0) random...
Can anyone help me with this problem? Thank you! 7. Let X1,.. , Xn denote a random sample from (1-9)/0 x; Test Ho: θ Bo versus H1: θ θο. (a) For a sample of size n, find a uniformly most powerful (UM...

Can anyone help me with this problem? Thank you! 7. Let X1,.. , Xn denote a random sample from (1-9)/0 x; Test Ho: θ Bo versus H1: θ θο. (a) For a sample of size n, find a uniformly most powerful (UMP) size-a test if such exists. (b) Take n-?, θ0-1, and α-.05, and sketch the power function of the UMP test. 7. Let X1,.. , Xn denote a random sample from (1-9)/0 x; Test Ho: θ Bo versus H1:...

Solve using the Neyman-Pearson Theorem 63. The error X in a measurement has a normal distri-...

Solve using the Neyman-Pearson Theorem 63. The error X in a measurement has a normal distri- bution with mean value 0 and variance o2. Con- sider testing Ho: a = 2 versus H: = 3 based on a random sample X1, . . . , X, of errors a. Show that a most powerful test rejects Ho when Σ>. b. For n 10, find the value of c for the test in (a) that results in a = .05
Let X1,...,Xn be a random sample from a Normal N(0, σ²). Consider Ho : σ² = 16 vs. Ha: σ² = 4. a)Use the Neyman Pearson...

Let X1,...,Xn be a random sample from a Normal N(0, σ²). Consider Ho : σ² = 16 vs. Ha: σ² = 4. a)Use the Neyman Pearson lemma to find the best critical region C*. b)If n = 10 and the size of the test is fixed as α = 0.10, find the critical region and the power when Ho is false.
(b) Let X have the pdf x? f(x)= ;-3<x<3, 18 = zero elsewhere. (i) Find the...

(b) Let X have the pdf x? f(x)= ;-3<x<3, 18 = zero elsewhere. (i) Find the cdf of X

Let (X1, ... , Xn) be an iid sample from the exponentially distributed X with pdf...

Let (X1, ... , Xn) be an iid sample from the exponentially distributed X with pdf given by f(x;0) = -e ô, x > 0, 0 >0. Use the Neyman-Pearson Lemma to find the a-level most powerful test (MPT) of Ho : 0 = 2 vs H : 0 = 3.
Let X1, . . . , Xn ∼ Exp(θ) and consider the test for H0 :...

Let X1, . . . , Xn ∼ Exp(θ) and consider the test for H0 : θ ≥ θ_0 vs H1 : θ < θ_0. (a) Find the size-α LRT. With rejection region, R = {sample mean > c} where c will depend on a value from the χ ^2 df=2n distribution. (b) Find the appropriate value of c.
Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find...

Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find c. b) Are X and Y independent? Why or why not? c) Find PX +Y05)

MA2500/18 8. Let X be a random variable and let 'f(r; θ) be its PDF where...

MA2500/18 8. Let X be a random variable and let 'f(r; θ) be its PDF where θ is an unknown scalar parameter. We wish to test the simple null hypothesis Ho: 0 against the simple alternative Hi : θ-64. (a) Define the simple likelihood ratio test (SLRT) of Ho against H (b) Show that the SLRT is a most powerful test of Ho against H. (c) Let Xi, X2.... , X be a random sample of observations from the Poisson(e)...

Find the Neyman-Pearson most powerful test of its size Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake

Homework Answers

Add Answer to:
Find the Neyman-Pearson most powerful test of its size Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake

Post as a guest

Earn Coins

3. Let Y be a random variable whose probability mass function under Ho and Hi is givern by 1 23 4 5 6 7 f(yHo) .01 01 01 01 01 01 94 fulHi) 06 0504 .03 02 01 79 Use the Neyman-Pearson Lemma to find...

please see picture 5. Let X1, X2,..., Xn be Bin(2,0) random variables with Θ {.45, .65). For testing Ho : θ 45 versus HA : θ-66, determine the following: (a) the form of the Neyman-Pearson MP crit...

Can anyone help me with this problem? Thank you! 7. Let X1,.. , Xn denote a random sample from (1-9)/0 x; Test Ho: θ Bo versus H1: θ θο. (a) For a sample of size n, find a uniformly most powerful (UM...

Solve using the Neyman-Pearson Theorem 63. The error X in a measurement has a normal distri-...

Let X1,...,Xn be a random sample from a Normal N(0, σ²). Consider Ho : σ² = 16 vs. Ha: σ² = 4. a)Use the Neyman Pearson...

(b) Let X have the pdf x? f(x)= ;-3<x<3, 18 = zero elsewhere. (i) Find the...

Let (X1, ... , Xn) be an iid sample from the exponentially distributed X with pdf...

Let X1, . . . , Xn ∼ Exp(θ) and consider the test for H0 :...

Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find...

MA2500/18 8. Let X be a random variable and let 'f(r; θ) be its PDF where...

Find the Neyman-Pearson most powerful test of its size Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake

Homework Answers

Add Answer to: Find the Neyman-Pearson most powerful test of its size Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake

Post as a guest

Earn Coins

Add Answer to:
Find the Neyman-Pearson most powerful test of its size Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake Let f(x: θ)-exp{-(x-θ)}, θ 4. and zero elsewhere. lake