4. Suppose that the random variable Y~U(0,θ). a. Use a transformation technique to show that W=Y/...

4. Suppose that the random variable Y~U(0,θ).

a. Use a transformation technique to show that W=Y/ θ is a pivotal quantity.

b. Use a. to find a 95% confidence interval for θ.

c. The time Clark walks into his Stats class is U(0,θ), where 0 represents 4:55pm, and time is measured in minutes after 4:55. If he shows up at 5:59 on a given day, use c. to find a 95% confidence interval for θ. Use two decimal places. Interpret the meaning of this interval.

d. DERIVE the pdf of Ymax, the maximum of a random sample of size 4 from U(0,θ).

Expert Solution

orchestra answered 2 years ago

Suppose Y~U(0,θ). a. Use the trasnformation technique to show that W=Y/θ. b. Find a 95% confidence...

Suppose Y~U(0,θ). a. Use the trasnformation technique to show that W=Y/θ. b. Find a 95% confidence interval for θ. c. Derive the pdf of Y_max of a random sample of size 4 from U(0,θ).

Please find a solution to the following: Δu=0, 1<r<4, 0≤θ<2π u(1,θ)=cos5θ, 0<θ<2π u(4,θ)=sin4θ, 0<θ<2π

Please find a solution to the following: Δu=0, 1<r<4, 0≤θ<2π u(1,θ)=cos5*θ, 0<θ<2π u(4,θ)=sin4*θ, 0<θ<2π

Let Y1, ..., Yn be a random sample with the pdf: f(y;θ)= θ(1-y)^(θ-1) with θ>0 and...

Let Y1, ..., Yn be a random sample with the pdf: f(y;θ)= θ(1-y)^(θ-1) with θ>0 and 0<y<1. i) Obtain the minimum variance unbiased estimator ( for θ)

Suppose that X1,. . . , Xn is an m.a. of a distribution U (0, θ]....

Suppose that X1,. . . , Xn is an m.a. of a distribution U (0, θ]. (a) Find the most powerful test of size α to test H0: θ = θ0 vs Ha: θ = θa, where θa <θ0. (b) Is the test obtained in part (a) the UMP (α) to test H0: θ = θ0 vs Ha: θ <θ0 ?. (c) Find the most powerful test of size α to test H0: θ = θ0 vs Ha: θ =...

For a random variable X with a Cauchy distribution with θ = 0 , so that...

For a random variable X with a Cauchy distribution with θ = 0 , so that f(x) =(1/ π)/( 1 + x^2) for -∞ < x < ∞ (a) Show that the expected value of the random variable X does not exist. (b) Show that the variance of the random variable X does not exist. (c) Show that a Cauchy random variable does not have ﬁnite moments of order greater than or equal to one.

Suppose γ is a random variable with Exp(θ) distribution. Conditioning on γ, Y ∼ Poisson(γ). Provide...

Suppose γ is a random variable with Exp(θ) distribution. Conditioning on γ, Y ∼ Poisson(γ). Provide the marginal mean and variance of Y

The random variable X is distributed with pdf fX(x, θ) = cxexp(-(x/θ)2), where x>0 and θ>0....

The random variable X is distributed with pdf fX(x, θ) = c*x*exp(-(x/θ)2), where x>0 and θ>0. a) What is the constant c? b) We consider parameter θ is a number. What is MLE and MOM of θ? Assume you have an i.i.d. sample. Is MOM unbiased? c) Please calculate the Crameer-Rao Lower Bound (CRLB). Compare the variance of MOM with Crameer-Rao Lower Bound (CRLB).

The random variable X is distributed with pdf fX(x, θ) = cxexp(-(x/θ)2), where x>0 and θ>0....

The random variable X is distributed with pdf fX(x, θ) = c*x*exp(-(x/θ)2), where x>0 and θ>0. a) Find the distribution of Y = (X1 + ... + Xn)/n where X1, ..., Xn is an i.i.d. sample from fX(x, θ). If you can’t find Y, can you find an approximation of Y when n is large? b) Find the best estimator, i.e. MVUE, of θ?

The random variable X is distributed with pdf fX(x, θ) = cxexp(-(x/θ)2), where x>0 and θ>0....

The random variable X is distributed with pdf fX(x, θ) = c*x*exp(-(x/θ)2), where x>0 and θ>0. (Please note the equation includes the term -(x/θ)2 or -(x/θ)^2 if you cannot read that) a) What is the constant c? b) We consider parameter θ is a number. What is MLE and MOM of θ? Assume you have an i.i.d. sample. Is MOM unbiased? c) Please calculate the Cramer-Rao Lower Bound (CRLB). Compare the variance of MOM with Crameer-Rao Lower Bound (CRLB).

The random variable X is distributed with pdffX(x, θ) = cxexp(-(x/θ)2), where x>0 and θ>0. (Please...

The random variable X is distributed with pdffX(x, θ) = c*x*exp(-(x/θ)2), where x>0 and θ>0. (Please note the equation includes the term -(x/θ)2 - that is -(x/θ)^2 if your computer doesn't work) a) What is the constant c? b) We consider parameter θ is a number. What is MLE and MOM of θ? Assume you have an i.i.d. sample. Is MOM unbiased? c) Please calculate the Cramer-Rao Lower Bound (CRLB). Compare the variance of MOM with Crameer-Rao Lower Bound (CRLB)....

Question

4. Suppose that the random variable Y~U(0,θ). a. Use a transformation technique to show that W=Y/...

Solutions

Expert Solution

Related Solutions

Suppose Y~U(0,θ). a. Use the trasnformation technique to show that W=Y/θ. b. Find a 95% confidence...

Please find a solution to the following: Δu=0, 1<r<4, 0≤θ<2π u(1,θ)=cos5θ, 0<θ<2π u(4,θ)=sin4θ, 0<θ<2π

Let Y1, ..., Yn be a random sample with the pdf: f(y;θ)= θ(1-y)^(θ-1) with θ>0 and...

Suppose that X1,. . . , Xn is an m.a. of a distribution U (0, θ]....

For a random variable X with a Cauchy distribution with θ = 0 , so that...

Suppose γ is a random variable with Exp(θ) distribution. Conditioning on γ, Y ∼ Poisson(γ). Provide...

The random variable X is distributed with pdf fX(x, θ) = cxexp(-(x/θ)2), where x>0 and θ>0....

The random variable X is distributed with pdf fX(x, θ) = cxexp(-(x/θ)2), where x>0 and θ>0....

The random variable X is distributed with pdf fX(x, θ) = cxexp(-(x/θ)2), where x>0 and θ>0....

The random variable X is distributed with pdffX(x, θ) = cxexp(-(x/θ)2), where x>0 and θ>0. (Please...