Problem 1. a. Suppose the two-dimensional continuous random variable (X,Y) has joint pdf £xx (x, y) = { fx 2x + 4y, 0
Problem 1. a. Suppose the two-dimensional continuous random variable (X,Y) has joint pdf £xx (x, y) = { fx 2x + 4y, 0
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Problem 1.
a. Suppose the two-dimensional continuous random variable (X, Y) has
joint pdf
{ 2,
2x+4y, 0<x< 1, 0 < y < 1/2
elsewhere.
fxy(x, y) = {
[i.] Find ƒx₁y(x|y).
[ii.] Let B = {X + Y ≥ 3/4}. Find P(B).
b. For n ≥ 2, let X₁, X2,..., Xn be i.i.d. samples from the the uniform
distribution U(0, 0 + 1) where is some real number. Let
X(1) ≤ X(2) ≤ · · · ≤ X(n)
be the order statistics of the sample.
Jimmi
[i.] Show that (X(1), X(n)) is a sufficient statistic for 0.
->
[ii.] Find an and b(0) such that an (b(0) - X(n)) → W in distribution,
where W has an exponential distribution with density f(w) = e, for
w> 0 and 0 elsewhere.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c304f9b-1d90-477c-aeed-2994e917417f%2Fc3f0e5eb-796f-4887-b7ee-f7fbd0550b58%2F8mmzqnv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1.
a. Suppose the two-dimensional continuous random variable (X, Y) has
joint pdf
{ 2,
2x+4y, 0<x< 1, 0 < y < 1/2
elsewhere.
fxy(x, y) = {
[i.] Find ƒx₁y(x|y).
[ii.] Let B = {X + Y ≥ 3/4}. Find P(B).
b. For n ≥ 2, let X₁, X2,..., Xn be i.i.d. samples from the the uniform
distribution U(0, 0 + 1) where is some real number. Let
X(1) ≤ X(2) ≤ · · · ≤ X(n)
be the order statistics of the sample.
Jimmi
[i.] Show that (X(1), X(n)) is a sufficient statistic for 0.
->
[ii.] Find an and b(0) such that an (b(0) - X(n)) → W in distribution,
where W has an exponential distribution with density f(w) = e, for
w> 0 and 0 elsewhere.
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