Suppose (Xn) is a sequence of iid random variables on R. Suppose that f is a density on R and suppose that for every a < b real numbers, n 1 [1 {X; € (a,b]} ª²> [ƒ(a) A(da) for Lebesgue measure A. Show that X₁ has density f.
Suppose (Xn) is a sequence of iid random variables on R. Suppose that f is a density on R and suppose that for every a < b real numbers, n 1 [1 {X; € (a,b]} ª²> [ƒ(a) A(da) for Lebesgue measure A. Show that X₁ has density f.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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![Suppose (Xn) is a sequence of iid random variables on R. Suppose
that f is a density on R and suppose that for every a < b real numbers,
n
1
a.s.
14
_1 {X; € (a, b)} => ["f
(a,b]} [
a
f(x) X(dx)
for Lebesgue measure A. Show that X₁ has density f.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F512f39ef-c7a2-453e-bd84-fdc3431b9e54%2F6114ace4-1b01-4d8d-8dcb-1780c614b808%2Fyt5cf8i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose (Xn) is a sequence of iid random variables on R. Suppose
that f is a density on R and suppose that for every a < b real numbers,
n
1
a.s.
14
_1 {X; € (a, b)} => ["f
(a,b]} [
a
f(x) X(dx)
for Lebesgue measure A. Show that X₁ has density f.
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