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...
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 =...
a.)Find the length of the spiral r=θ for 0 ≤ θ ≤ 2
b.)Find the exact length of the polar curve r=3sin(θ), 0 ≤ θ ≤
π/3
c.)Write each equation in polar coordinates. Express as a
function of t. Assume that r>0.
- y=(−9)
r=
- x^2+y^2=8
r=
- x^2 + y^2 − 6x=0
r=
- x^2(x^2+y^2)=2y^2
r=
Let X1,...,Xn ∼ Geo(θ).
(a) Find a 90% asymptotic confidence interval for θ.
(b) Find a 99% asymptotic lower confidence intervals for φ =
1/θ, the expected number of trials until the first success.
Suppose U is uniform on (0,1). Let Y = U(1 − U). (a) Find P(Y
> y) for 0 < y < 1/4. (b) differentiate to get the density
function of Y . (c) Find an increasing function g(u) so that g(U )
has the same distribution as U (1 − U ).
data set
yes 27 no 4
find the 95% and 99% confidence intervals for u
find the 95% and 99% confidence intervals for o
find the 95% and 99% confidense intervals for p
If consumption is C = a + b(Y – T) – θr, where θ > 0, then,
other things equal, monetary policy is more effective, and fiscal
policy is less effective, in changing the level of output compared
to when consumption is given by a standard Keynesian consumption
function of the form C = a + b(Y – T).