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(g) (e) and (f) the last 4 questions are what i need help
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Problem(12)...
F(,r,), that is, W has an F distribution with 1) (a) How to define a r.v....
F(,r,), that is, W has an F distribution with 1) (a) How to define a r.v. W so that W n and r, degrees of freedom ? Now, let W F(r, 7). (3%) (b) What is the distribution of (2%) (c) Let F(,) be the upper a th quantile of the distribution of W. P(Wz F_(n,F))= a. (0<a<1). Prove that F.(.) = F_(r. ,r.) That is, I (%9) (d) Find P(F,, (,)sWs Fou i,)) (4%) 2) (a) How to define...
4. Exercise Let X, Y be RVs. Denote E[X] = Hy and E[Y] =py. Suppose we...
4. Exercise Let X, Y be RVs. Denote E[X] = Hy and E[Y] =py. Suppose we want to test the null hypothesis Ho : Mx = uy against the alternative hypothesis Hi : 4x > uy. Suppose we have i.i.d. pairs (X1,Yı),...,(Xn, Yn) from the joint distribution of (X,Y). Further assume that we know the X - Y follows a normal distribution. (i) Show that exactly) T:= (X-Y)-(ux-uy) - tn-1), Sin (3) where s2 = n-1 [?-,((X; – Y;) –...
(b) and (c) are what i need help with Problem(7) Let z Student's t-distribution. The density...
(b)
and (c) are what i need help with
Problem(7) Let z Student's t-distribution. The density function of T is Normal(0, 1) and Y ~ xã, then the new r.v. T = Jun has the r[(y + 1)/2) -(4+1)/2 fr(t) = + (7/2) (a) (3 points) Describe the similarity/difference between T and Z. (b) (6 points) Let to be a particular value of t. Use t-distribution table to find to values such that the following statements are true. (Given that...
need help with e,f,g Let W be the weight of the ith airline passenger's luggage. Assume...
need help with e,f,g
Let W be the weight of the ith airline passenger's luggage. Assume that the weights are independent, cach with pdf f(w) - B-w-1 ifo <w<B and zero otherwise. (a) For n=100, = 3, and B = 80, approximate P W (b) If W is the smallest value out of, then show that w a s n . (c) If W, is the largest value out of, then show that W B as n . (d) Find...
Exercise 4 (Paired test, known normality of the difference). Let X, Y be RVs. Denote E[X]...
Exercise 4 (Paired test, known normality of the difference). Let X, Y be RVs. Denote E[X] = 4x and E[Y] = uy. Suppose we want to test the null hypothesis Houx = My against the alternative hy- pothesis H ux #uy. Suppose we have i.i.d. pairs (X1,Y),...,(X,Y) from the joint distribution of (X,Y). Further assume that we know the X - Y follows a normal distribution. (i) Noting that X1 - Y1,..., Xn-Ynare i.i.d. with normal distribution, show that (exactly)...
4. Let 8 >0. Let X, X2,..., X, be a random sample from the distribution with...
4. Let 8 >0. Let X, X2,..., X, be a random sample from the distribution with probability density function S(*;ð) - ma t?e-vor x>0, zero otherwise. Recall: W=vX has Gamma( a -6, 0-ta) distribution. Y=ZVX; = Z W; has a Gamma ( a =6n, = ta) distribution. i=1 E(Xk) - I( 2k+6) 120 ok k>-3. 42 S. A method of moments estimator of 8 is 42.n 8 = h) Suggest a confidence interval for 8 with (1 - 0) 100%...
In the simple linear regression with zero-constant item for (xi , yi) where i = 1, 2, · · · , n, Yi = βxi + i where {i} n i=1 are i.i.d. N(0, σ2 ). (a) Derive the normal equation that the LS estimator...
In the simple linear regression with zero-constant item for (xi , yi) where i = 1, 2, · · · , n, Yi = βxi + i where {i} n i=1 are i.i.d. N(0, σ2 ). (a) Derive the normal equation that the LS estimator, βˆ, satisfies. (b) Show that the LS estimator of β is given by βˆ = Pn i=1 P xiYi n i=1 x 2 i . (c) Show that E(βˆ) = β, V ar(βˆ) = σ...
for these questions I need help on just the questions on all of them where it...
for these questions I need help on just the questions on all of them where it says "what is the value of the sample test statistic?" 24.) The average annual miles driven per vehicle in the United States is 11.1 thousand miles, with σ ≈ 600 miles. Suppose that a random sample of 36 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.9thousand miles. Does this indicate that the average miles driven per...
Degrees of Freedom of a Known Test 2 points possible graded) Let us consider a statistical...
Degrees of Freedom of a Known Test 2 points possible graded) Let us consider a statistical model with parameter ER". Let O be the parameter that generates the n lid samples X1,..., X, Let I ) be the Fisher information and assume that the MLE is asymptotically normal. Assume that I(C) is a diagonal matrix with positive entries 1/t1,...,1/td. We wish to perform a test for the hypotheses H : 8 - and H:8 + . Let the test statistic...
help with d,e,f,g,h,i A die is rolled 120 times to see if it is fair. The...
help with d,e,f,g,h,i
A die is rolled 120 times to see if it is fair. The table below shows the frequencies for each of the six possible outcomes. Use a level of significance of a = 0.05. a. Complete the rest of the table by filling in the expected frequencies (enter your answers in fraction form): Ex Frequency of Dice Values Outcome Frequency Expected Frequency 29 20 2 23 20 3 17 20 4 10 20 5 23 20 С...
F(,r,), that is, W has an F distribution with 1) (a) How to define a r.v. W so that W n and r, degrees of freedom ? Now, let W F(r, 7). (3%) (b) What is the distribution of (2%) (c) Let F(,) be the upper a th quantile of the distribution of W. P(Wz F_(n,F))= a. (0<a<1). Prove that F.(.) = F_(r. ,r.) That is, I (%9) (d) Find P(F,, (,)sWs Fou i,)) (4%) 2) (a) How to define...
4. Exercise Let X, Y be RVs. Denote E[X] = Hy and E[Y] =py. Suppose we want to test the null hypothesis Ho : Mx = uy against the alternative hypothesis Hi : 4x > uy. Suppose we have i.i.d. pairs (X1,Yı),...,(Xn, Yn) from the joint distribution of (X,Y). Further assume that we know the X - Y follows a normal distribution. (i) Show that exactly) T:= (X-Y)-(ux-uy) - tn-1), Sin (3) where s2 = n-1 [?-,((X; – Y;) –...
(b)
and (c) are what i need help with
Problem(7) Let z Student's t-distribution. The density function of T is Normal(0, 1) and Y ~ xã, then the new r.v. T = Jun has the r[(y + 1)/2) -(4+1)/2 fr(t) = + (7/2) (a) (3 points) Describe the similarity/difference between T and Z. (b) (6 points) Let to be a particular value of t. Use t-distribution table to find to values such that the following statements are true. (Given that...
need help with e,f,g
Let W be the weight of the ith airline passenger's luggage. Assume that the weights are independent, cach with pdf f(w) - B-w-1 ifo <w<B and zero otherwise. (a) For n=100, = 3, and B = 80, approximate P W (b) If W is the smallest value out of, then show that w a s n . (c) If W, is the largest value out of, then show that W B as n . (d) Find...
Exercise 4 (Paired test, known normality of the difference). Let X, Y be RVs. Denote E[X] = 4x and E[Y] = uy. Suppose we want to test the null hypothesis Houx = My against the alternative hy- pothesis H ux #uy. Suppose we have i.i.d. pairs (X1,Y),...,(X,Y) from the joint distribution of (X,Y). Further assume that we know the X - Y follows a normal distribution. (i) Noting that X1 - Y1,..., Xn-Ynare i.i.d. with normal distribution, show that (exactly)...
4. Let 8 >0. Let X, X2,..., X, be a random sample from the distribution with probability density function S(*;ð) - ma t?e-vor x>0, zero otherwise. Recall: W=vX has Gamma( a -6, 0-ta) distribution. Y=ZVX; = Z W; has a Gamma ( a =6n, = ta) distribution. i=1 E(Xk) - I( 2k+6) 120 ok k>-3. 42 S. A method of moments estimator of 8 is 42.n 8 = h) Suggest a confidence interval for 8 with (1 - 0) 100%...
Degrees of Freedom of a Known Test 2 points possible graded) Let us consider a statistical model with parameter ER". Let O be the parameter that generates the n lid samples X1,..., X, Let I ) be the Fisher information and assume that the MLE is asymptotically normal. Assume that I(C) is a diagonal matrix with positive entries 1/t1,...,1/td. We wish to perform a test for the hypotheses H : 8 - and H:8 + . Let the test statistic...
help with d,e,f,g,h,i
A die is rolled 120 times to see if it is fair. The table below shows the frequencies for each of the six possible outcomes. Use a level of significance of a = 0.05. a. Complete the rest of the table by filling in the expected frequencies (enter your answers in fraction form): Ex Frequency of Dice Values Outcome Frequency Expected Frequency 29 20 2 23 20 3 17 20 4 10 20 5 23 20 С...
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