Reference no: EM13993273
1. Let X., X2 , • • • , X11 be a random sample from a Poisson distribution with mean 0. Find the unbiased minimum variance estimator of 02.
2. We consider a random sample X1 , X2 , • • • , X11 from a distribution with p.d.f./(x; ()) = (l/0) exp ( -x/0), 0 <>x <>oo, zero elsewhere, where O 0. Possibly, in a life testing situation, however, we only observe the first r order statistics, Y1 <>Y2 <>··· Yr-
(a) Record the joint p.d.f. of these order statistics and denote it by L(O).
(b) Under these conditions, find the m.l.e., 0, by maximizing L(O).
(c) Find the m.g.f. and p.d.f. of 0. .
(d) With a slight extension of the definition of sufficiency, is O a sufficient statistic?
(e) Find the unbiased minimum variance estimator for 0.
(f) Show that Y1 /8 and tJ are independent.
|
Poisson distribution with parameter
: 1. Let X have a Poisson distribution with parameter 0. Assume that the unknown O is a value of a random variable 0 that has a gamma distribution with parameters IX = r and fJ = (1 -p)/ p, where r is a positive integer and 0 p 1.
|
|
Estimate the current and future water demand
: Based on the average property occupancy rate in this region, estimate the current population of this community - Estimate the current and future water demand for years 2025, 2035 and 2045.
|
|
Distribution with r degrees of freedom
: Let X be N(O, 1/0). Assume that the unknown O is a value of a random variable 0 which has a gamma distribution with parameters IX = r/2 and fJ = 2/r, where r is a positive integer. Show that X has a marginal I-distribution with r degrees of freed..
|
|
Primary cause of heartburn and constipation
: The primary cause of heartburn and constipation during pregnancy is
|
|
Random sample from a poisson distribution
: 1. Let X., X2 , • • • , X11 be a random sample from a Poisson distribution with mean 0. Find the unbiased minimum variance estimator of 02.
|
|
Which of the following best describes exercise
: Which of the following BEST describes exercise? Which of the following sports is the least likely to place a young girl or woman at risk for the female athlete triad
|
|
What is its kinetic energy in ev
: If the position of a chlorine ion in a membrane is measured to an accuracy of 5.00 μm, what is its minimum uncertainty in velocity, given its mass is 5.86 x 10-26 kg? If the ion has this velocity, what is its kinetic energy in eV? (Compare this wi..
|
|
Why osteoporosis incidents in the united states
: What is the primary reason why osteoporosis incidents in the United States are expected to increase
|
|
Problem regarding the degrees of freedom
: (a) Argue that the ratio R = (X + Xi)/(Xi + · ··+ ..¥;) and its denomi nator (Xi + ··· + ..¥;) are independent. (b) Does SR/ 2 have an £-distribution with 2 and S degrees of freedom? Explain your answer. (c) Compute E(R) using Exercise 7.6..
|