Homework Answers
uploaded exercise 2 for reference 4. First write a program that achieves the same result as...
uploaded exercise 2 for reference
4. First write a program that achieves the same result as in Exercise 2 but using a while loop. Then write a program that does this using vector operations (and no loops). If it doesn't already, make sure your program works for the case a 1 2. Let h(z, n) = 1 + x + x2 + +z" = Σ'=0a". Write an R program to calculate h(z, n) using a for loop
attached exercise 2 below for reference. 4. First write a program that achieves the same result...
attached exercise 2 below for reference.
4. First write a program that achieves the same result as in Exercise 2 but using a while loop. Then write a program that does this using vector operations (and no loops). If it doesn't already, make sure your program works for the case a 1 2. Let h(z, n) = 1 + x + x2 + +z" = Σ'=0a". Write an R program to calculate h(z, n) using a for loop
2. Let h(z, n) = 1 + x + x2 + +z" = Σ'=0a". Write an...
2. Let h(z, n) = 1 + x + x2 + +z" = Σ'=0a". Write an R program to calculate h(z, n) using a for loop
3. Let Xi, . . . , Xn be random samples of X and X(1), ....
3. Let Xi, . . . , Xn be random samples of X and X(1), . . . , X(n) ordered random samples of X which are obtained from a rearrangement of X1,... , Xn such that (a) Show that the empirical distribution functions of Xi,..., Xn and Xo),..., X(n) coincide. (b) Consider the samples taken from X ~ F. Use (a) to compute A-2), F,,(-1)Ћ,(1.8),Ћ,(25) (c) (Continued from (b)) Plot A,(z) over-2 4.
2a) Let a, b e R with a < b and let g [a, bR be...
2a) Let a, b e R with a < b and let g [a, bR be continuous. Show that g(x) cos(nx) dx→ 0 n →oo. as Hint: Let ε > 0, By uniform continuity of g, there exists δ > 0 such that 2(b - a Choose points a = xo < x1 < . . . < Xm such that Irh-1-2k| < δ. Then we may write rb g (z) cos(nx) dx = An + Bn where 7m (g(x)...
2. (40 pts) Let fn: RR be given by sin(n) In(x) = n2 NEN. 2a. (10...
2. (40 pts) Let fn: RR be given by sin(n) In(x) = n2 NEN. 2a. (10 pts) Show that the series 2n=1 fn converges uniformly on R. 2b. (10 pts) Show that the function f: RR, f (x) = sin (nx) n2 n=1 is continuous on R. 2c. (10 pts) Show that f given in 2b) is intergrable and $(z)de = 24 (2n-1) 2d. (10 pts) Let 0 <ö< be given. Show that f given in 2b) is differentiable at...
(1) Let P denote the solid bounded by the surface of the hemisphere z -Vl-r-y? and the cone2y2 and let n denote an outw...
(1) Let P denote the solid bounded by the surface of the hemisphere z -Vl-r-y? and the cone2y2 and let n denote an outwardly directed unit normal vector. Define the vector field F(x, y, z) = yi + zVJ + 21k. (a) Evaluate the surface integral F n dS directly without using Gauss' Divergence Theorem. (b) Evaluate the triple integral Ш div(F) dV directly without using Gauss' Diver- gence Theorem Note: You should obtain the same answer in (a) and...
Let Xi, , Xn be a random sample from a n(o, σ*) distribution with pdf given by 2πσ I. Is the dist...
Let Xi, , Xn be a random sample from a n(o, σ*) distribution with pdf given by 2πσ I. Is the distribution family {f(x; σ), σ 0} complete? 2. Is PCH)〈1) the same for all σ ? 3. Find a sufficient statistic for σ. 4. Is the sufficient statistic from (c) also complete!?
Let Xi, , Xn be a random sample from a n(o, σ*) distribution with pdf given by 2πσ I. Is the distribution family {f(x; σ), σ 0}...
Problem 2 (20p). For each n E N, let Xn : Ω → R be a randon variable on a probability space (Q,F, P) with the exponential distribution n. Does there exist a randon variable X : Ω-+ R such that Xn → X...
Problem 2 (20p). For each n E N, let Xn : Ω → R be a randon variable on a probability space (Q,F, P) with the exponential distribution n. Does there exist a randon variable X : Ω-+ R such that Xn → X as n → oo? e a random variable on a probability space
Problem 2 (20p). For each n E N, let Xn : Ω → R be a randon variable on a probability space (Q,F, P)...
3. Let Xi, , Xn be i.i.d. Lognormal(μ, σ2) (a) Suppose σ-1, prove that S-X(n)/X(i) is an ancillar...
3. Let Xi, , Xn be i.i.d. Lognormal(μ, σ2) (a) Suppose σ-1, prove that S-X(n)/X(i) is an ancillary statistics. (b) Suppose p 0, prove T-X(n) is a sufficient and complete statistics (c) Find a minimal sufficient statistics.
3. Let Xi, , Xn be i.i.d. Lognormal(μ, σ2) (a) Suppose σ-1, prove that S-X(n)/X(i) is an ancillary statistics. (b) Suppose p 0, prove T-X(n) is a sufficient and complete statistics (c) Find a minimal sufficient statistics.
uploaded exercise 2 for reference
4. First write a program that achieves the same result as in Exercise 2 but using a while loop. Then write a program that does this using vector operations (and no loops). If it doesn't already, make sure your program works for the case a 1 2. Let h(z, n) = 1 + x + x2 + +z" = Σ'=0a". Write an R program to calculate h(z, n) using a for loop
attached exercise 2 below for reference.
4. First write a program that achieves the same result as in Exercise 2 but using a while loop. Then write a program that does this using vector operations (and no loops). If it doesn't already, make sure your program works for the case a 1 2. Let h(z, n) = 1 + x + x2 + +z" = Σ'=0a". Write an R program to calculate h(z, n) using a for loop
2. Let h(z, n) = 1 + x + x2 + +z" = Σ'=0a". Write an R program to calculate h(z, n) using a for loop
3. Let Xi, . . . , Xn be random samples of X and X(1), . . . , X(n) ordered random samples of X which are obtained from a rearrangement of X1,... , Xn such that (a) Show that the empirical distribution functions of Xi,..., Xn and Xo),..., X(n) coincide. (b) Consider the samples taken from X ~ F. Use (a) to compute A-2), F,,(-1)Ћ,(1.8),Ћ,(25) (c) (Continued from (b)) Plot A,(z) over-2 4.
2a) Let a, b e R with a < b and let g [a, bR be continuous. Show that g(x) cos(nx) dx→ 0 n →oo. as Hint: Let ε > 0, By uniform continuity of g, there exists δ > 0 such that 2(b - a Choose points a = xo < x1 < . . . < Xm such that Irh-1-2k| < δ. Then we may write rb g (z) cos(nx) dx = An + Bn where 7m (g(x)...
2. (40 pts) Let fn: RR be given by sin(n) In(x) = n2 NEN. 2a. (10 pts) Show that the series 2n=1 fn converges uniformly on R. 2b. (10 pts) Show that the function f: RR, f (x) = sin (nx) n2 n=1 is continuous on R. 2c. (10 pts) Show that f given in 2b) is intergrable and $(z)de = 24 (2n-1) 2d. (10 pts) Let 0 <ö< be given. Show that f given in 2b) is differentiable at...
(1) Let P denote the solid bounded by the surface of the hemisphere z -Vl-r-y? and the cone2y2 and let n denote an outwardly directed unit normal vector. Define the vector field F(x, y, z) = yi + zVJ + 21k. (a) Evaluate the surface integral F n dS directly without using Gauss' Divergence Theorem. (b) Evaluate the triple integral Ш div(F) dV directly without using Gauss' Diver- gence Theorem Note: You should obtain the same answer in (a) and...
Let Xi, , Xn be a random sample from a n(o, σ*) distribution with pdf given by 2πσ I. Is the distribution family {f(x; σ), σ 0} complete? 2. Is PCH)〈1) the same for all σ ? 3. Find a sufficient statistic for σ. 4. Is the sufficient statistic from (c) also complete!?
Let Xi, , Xn be a random sample from a n(o, σ*) distribution with pdf given by 2πσ I. Is the distribution family {f(x; σ), σ 0}...
Problem 2 (20p). For each n E N, let Xn : Ω → R be a randon variable on a probability space (Q,F, P) with the exponential distribution n. Does there exist a randon variable X : Ω-+ R such that Xn → X as n → oo? e a random variable on a probability space
Problem 2 (20p). For each n E N, let Xn : Ω → R be a randon variable on a probability space (Q,F, P)...
3. Let Xi, , Xn be i.i.d. Lognormal(μ, σ2) (a) Suppose σ-1, prove that S-X(n)/X(i) is an ancillary statistics. (b) Suppose p 0, prove T-X(n) is a sufficient and complete statistics (c) Find a minimal sufficient statistics.
3. Let Xi, , Xn be i.i.d. Lognormal(μ, σ2) (a) Suppose σ-1, prove that S-X(n)/X(i) is an ancillary statistics. (b) Suppose p 0, prove T-X(n) is a sufficient and complete statistics (c) Find a minimal sufficient statistics.
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