![Problem 2: Consider two probability density function on [0,1] : fo(x) = 1 and fi(x) = 2x (a) Construct the most powerful test](http://img.homeworklib.com/questions/8acdabd0-71c8-11ec-9918-716ba8b07765.png?x-oss-process=image/resize,w_560)
Homework Answers
![the MP pest is the hypothesis To test the hypothesis &= f (2) k 7th (2) 0; ow with E. [9] 0.1 o k > > f, (*) tho(a) [&] = 0.1](http://img.homeworklib.com/questions/8b70ea70-71c8-11ec-b20e-f797556fe0b5.png?x-oss-process=image/resize,w_560)
Add Answer to:
Problem 2: Consider two probability density function on [0,1] : fo(x) = 1 and fi(x) =...
1. Consider two probability density functions on [0,1]: f0(x) = 3x2 and f1(x) = 4x3. a.)...
1. Consider two probability density functions on [0,1]: f0(x) = 3x2 and f1(x) = 4x3. a.) Construct the most powerful test for H0 : X ~ f0 against HA : X ~ f1 with the significance level alpha = 0.1 b.) Find its power.
5. Suppose X a single observation from a population with a Beta(0,1) distribution. (a) Suppose we...
5. Suppose X a single observation from a population with a Beta(0,1) distribution. (a) Suppose we want to test Ho :0 <1 against H :0>1 an we use a rejection region of X > 1/2. Find the size and power function for this test. Sketch the power function. (b) Now suppose we want to test H, :0 = 1 against H :0 = 2. Find the most powerful level a test. (Is there a Theorem we can use?) (C) Is...
Problem 5 (15pts). Suppose that we observe a random sample X. from the density Xn 1 0 2 0, else, where m is a known constant which is greater than zero, and 0>0. (a) Find the most powerful test...
Problem 5 (15pts). Suppose that we observe a random sample X. from the density Xn 1 0 2 0, else, where m is a known constant which is greater than zero, and 0>0. (a) Find the most powerful test for testing Ho : θ Bo against b) Indicate how you would find the power of the most powerful test when θ-e-Do not perform (c) Is the resulting test uniformly most powerful for testing Ho :0-00 against Ha :e> et Explain...
You have observed one observation X from a distribution with probability density function fx (x) ...
You have observed one observation X from a distribution with probability density function fx (x) and support X = {x : 0 〈 x 〈 1} (a) Derive the most powerful α 0.05 test for testing Ho : fx(x) = 2x 1 (0 < x < 1) versus H1 : fx (x) = 5c4 1 (0 〈 x 〈 1). Be sure to give the rejection region explicitly. (b) Compute the power of the test
You have observed one observation...
parametric distribution 2. Let observations X, , ,X" be iid with a density function f. We...
parametric distribution
2. Let observations X, , ,X" be iid with a density function f. We would like to test for Ho :f=fo versus Hi : f关fo, where a form of fo is known. 2.1 Show that in this statement of the problem there are no most powerful tests. equivalent to testing the uniformity of f which the test is based. 2.2 Assume fo is completely known; prove that to test for Ho is 2.3 Research one test for normality...
7. You have one observation Y , which has one of the discrete pdf’s y f0(y)...
7. You have one observation Y , which has one of the discrete pdf’s
y f0(y) f1(y) 0 0.1 0.3 1 0.1 0.1 2 0.1 0.1 3 0.1 0.2 4 0.2 0.1 5
0.1 0.1 6 0.3 0.1 You want to test H0 : f0 is true Ha : f1 is true
(a) Here is a test: reject H0 if Y = 0, 1, 2, 3, or 5. What are the
probabilities of the two types of error for this...
The random variable X has two possible distributions: fo(x) = ze-z?/21(x > 0) or a2 /2 (a) Find t...
The random variable X has two possible distributions: fo(x) = ze-z?/21(x > 0) or a2 /2 (a) Find the most powerful level α-0.05 test of Ho : X ~ 0(x) versus H1 : X ~ fı(x) on the basis of observing X only b) Calculate the power of your test in part (a).
The random variable X has two possible distributions: fo(x) = ze-z?/21(x > 0) or a2 /2 (a) Find the most powerful level α-0.05 test of Ho :...
If X ~ N(0, σ2), then Y function of Y is X follows a half-normal distribution; i.e., the probabil...
If X ~ N(0, σ2), then Y function of Y is X follows a half-normal distribution; i.e., the probability density This population level model might arise, for example, if X measures some type of zero-mean difference (e.g., predicted outcome from actual outcome) and we are interested in absolute differences. Suppose that Yi, ½, ,y, is an iid sample from fy(ylơ2) (a) Derive the uniformly most powerful (UMP) level α test of 2 2 0 versus Identify all critical values associated...
5. Suppose Y represents a single observation from the probability density function given by: Soyo-1, 0,...
5. Suppose Y represents a single observation from the probability density function given by: Soyo-1, 0, 0<y<1 elsewhere Find the most powerful test with significance level a=0.05 to test: HO: 0=1 vs. Ha: 0=2.
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question:...
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question: Fact 1: If X EXP(0) then 2X/0~x(2). Fact 2: If V V, are a random sample from a x2(k) distribution then V V (nk) (a) Suppose that we wish to test Ho : 0 against H : 0 = 0, where 01 is specified and 0, > Oo. Show that the likelihood ratio statistic AE, O0,0)f(E)/ f (x;0,)...
5. Suppose X a single observation from a population with a Beta(0,1) distribution. (a) Suppose we want to test Ho :0 <1 against H :0>1 an we use a rejection region of X > 1/2. Find the size and power function for this test. Sketch the power function. (b) Now suppose we want to test H, :0 = 1 against H :0 = 2. Find the most powerful level a test. (Is there a Theorem we can use?) (C) Is...
Problem 5 (15pts). Suppose that we observe a random sample X. from the density Xn 1 0 2 0, else, where m is a known constant which is greater than zero, and 0>0. (a) Find the most powerful test for testing Ho : θ Bo against b) Indicate how you would find the power of the most powerful test when θ-e-Do not perform (c) Is the resulting test uniformly most powerful for testing Ho :0-00 against Ha :e> et Explain...
You have observed one observation X from a distribution with probability density function fx (x) and support X = {x : 0 〈 x 〈 1} (a) Derive the most powerful α 0.05 test for testing Ho : fx(x) = 2x 1 (0 < x < 1) versus H1 : fx (x) = 5c4 1 (0 〈 x 〈 1). Be sure to give the rejection region explicitly. (b) Compute the power of the test
You have observed one observation...
parametric distribution
2. Let observations X, , ,X" be iid with a density function f. We would like to test for Ho :f=fo versus Hi : f关fo, where a form of fo is known. 2.1 Show that in this statement of the problem there are no most powerful tests. equivalent to testing the uniformity of f which the test is based. 2.2 Assume fo is completely known; prove that to test for Ho is 2.3 Research one test for normality...
7. You have one observation Y , which has one of the discrete pdf’s
y f0(y) f1(y) 0 0.1 0.3 1 0.1 0.1 2 0.1 0.1 3 0.1 0.2 4 0.2 0.1 5
0.1 0.1 6 0.3 0.1 You want to test H0 : f0 is true Ha : f1 is true
(a) Here is a test: reject H0 if Y = 0, 1, 2, 3, or 5. What are the
probabilities of the two types of error for this...
The random variable X has two possible distributions: fo(x) = ze-z?/21(x > 0) or a2 /2 (a) Find the most powerful level α-0.05 test of Ho : X ~ 0(x) versus H1 : X ~ fı(x) on the basis of observing X only b) Calculate the power of your test in part (a).
The random variable X has two possible distributions: fo(x) = ze-z?/21(x > 0) or a2 /2 (a) Find the most powerful level α-0.05 test of Ho :...
If X ~ N(0, σ2), then Y function of Y is X follows a half-normal distribution; i.e., the probability density This population level model might arise, for example, if X measures some type of zero-mean difference (e.g., predicted outcome from actual outcome) and we are interested in absolute differences. Suppose that Yi, ½, ,y, is an iid sample from fy(ylơ2) (a) Derive the uniformly most powerful (UMP) level α test of 2 2 0 versus Identify all critical values associated...
5. Suppose Y represents a single observation from the probability density function given by: Soyo-1, 0, 0<y<1 elsewhere Find the most powerful test with significance level a=0.05 to test: HO: 0=1 vs. Ha: 0=2.
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question: Fact 1: If X EXP(0) then 2X/0~x(2). Fact 2: If V V, are a random sample from a x2(k) distribution then V V (nk) (a) Suppose that we wish to test Ho : 0 against H : 0 = 0, where 01 is specified and 0, > Oo. Show that the likelihood ratio statistic AE, O0,0)f(E)/ f (x;0,)...
Most questions answered within 3 hours.
-
How much must I invest today if I want to withdraw 1/3 of my
original investment...
asked 33 minutes ago -
What is meant by a “term premium”?
What can explain such a premium? Is it a...
asked 2 hours ago -
23. Which molecule has only covalent bonds? A. CO2 B. Al2O3 C.
Mg3N2
24. The octet...
asked 2 hours ago -
the
total pressure for a mixture of N2O4 and NO2 is 2.20 atm. If Kp=
7.10...
asked 2 hours ago -
Delaware Corp. prepared a master budget that included $22,385
for direct materials, $28,600 for direct labor,...
asked 2 hours ago -
For pesticide HCB (hexachlorobenzene), its logarithmic partition
coefficient log Kow is 5.6. What would be the...
asked 2 hours ago -
A chemist requires 0.422 mil Na2CO3 for a reaction. How many
grams does this correspond to?
asked 2 hours ago -
If the vapor pressure of carvone is approximately 9.4 torr at 99
°C, approximately how much...
asked 3 hours ago -
A juice bottling company is carrying out a test at 10%
significance that the mean population...
asked 3 hours ago -
What is the reflectivity (in percent) needed to keep water at a
temperature near its freezing...
asked 3 hours ago -
Suppose that the average surface temperature of Earth is 300K.
Assume this is uniform over its...
asked 3 hours ago -
Draw the condensed structural formula for alkenes and alkynes or
the line-angle structural formula for cycloalkenes...
asked 3 hours ago