Let y be the variable of interest, and x be an auxiliary variable. Show that the...

Let y be the variable of interest, and x be an auxiliary variable. Show that the RSS (Ranked Set Sampling) estimator for y mean is an unbiased estimator of the population mean.

Expert Solution

Answers:

The process for computing RSS (Ranked Set Sampling) estimator for y mean is an unbiased estimator of the population mean is below:

The above process in images shown the RSS (Ranked Set Sampling) estimator for y mean is an unbiased estimator of the population mean.

orchestra answered 1 year ago

(a) Let X be a binomial random variable with parameters (n, p). Let Y be a...

(a) Let X be a binomial random variable with parameters (n, p). Let Y be a binomial random variable with parameters (m, p). What is the pdf of the random variable Z=X+Y? (b) Let X and Y be indpenednet random variables. Let Z=X+Y. What is the moment generating function for Z in terms of those for X and Y? Confirm your answer to the previous problem (a) via moment generating functions.

Let the random variable X and Y have the joint pmf f(x, y) = , c...

Let the random variable X and Y have the joint pmf f(x, y) = , c xy 2 where x = 1, 2, 3; y = 1, 2, x + y ≤ 4 , that is, (x, y) are {(1, 1),(1, 2),(2, 1),(2, 2),(3, 1)} . (a) Find c > 0 . (b) Find μ . X (c) Find μ . Y (d) Find σ . 2 X (e) Find σ . 2 Y (f) Find Cov (X, Y )...

Let X, Y be independent exponential random variables with mean one. Show that X/(X + Y...

Let X, Y be independent exponential random variables with mean one. Show that X/(X + Y ) is uniformly distributed on [0, 1]. (Please solve it with clear explanations so that I can learn it. I will give thumbs up.)

Let the random variable and have the joint pmf X Y f(x,y) = {x(y)^2}/c where x...

Let the random variable and have the joint pmf X Y f(x,y) = {x(y)^2}/c where x = 1, 2, 3 ; y = 1, 2, x+y<= 4, that is (x,y) are {(1,1), (1,2), (2,1), (2,2), 3,1)} (a) Find . c > 0 (b) Find . μX (c) Find . μY (d) Find . σ2 X (e) Find . σ2 Y (f) Find Cov . (X,Y ) (g) Find p , Corr . (x,y) (h) Are and X and Y independent

Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to...

Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to the power of Y. What is the distribution of Z?

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )

2. Let X be a uniform random variable over the interval (0, 1). Let Y =...

2. Let X be a uniform random variable over the interval (0, 1). Let Y = X(1-X). a. Derive the pdf for Y . b. Check the pdf you found in (a) is a pdf. c. Use the pdf you found in (a) to find the mean of Y . d. Compute the mean of Y by using the distribution for X. e. Use the pdf of Y to evaluate P(|x-1/2|<1/8). You cannot use the pdf for X. f. Use...

Let f: X-->Y and g: Y-->Z be arbitrary maps of sets (a) Show that if f...

Let f: X-->Y and g: Y-->Z be arbitrary maps of sets (a) Show that if f and g are injective then so is the composition g o f (b) Show that if f and g are surjective then so is the composition g o f (c) Show that if f and g are bijective then so is the composition g o f and (g o f)^-1 = g ^ -1 o f ^ -1 (d) Show that f: X-->Y is...

A random variable X is Normally distributed with mean = 75 and = 8. Let Y...

A random variable X is Normally distributed with mean = 75 and = 8. Let Y be a second Normally distributed random variable with mean = 70 and = 12. It is also known that X and Y are independent of one another. Let W be a random variable that is the difference between X and Y (i.e., W = X – Y). What can be said about the distribution of W?

Let X and Y be random variables with finite means. Show that min g(x) E(Y−g(X))^2=E(Y−E(Y|X))^2 Hint:...

Let X and Y be random variables with finite means. Show that min g(x) E(Y−g(X))^2=E(Y−E(Y|X))^2 Hint: a−b = a−c+c−b

Question