Let f(x) be a continuous function on [0, 1] and consider the limit 1 Xj +... f + In · drn. lim dx1 ... ... n00 Give (1) a probabilistic interpretation by interpreting the integration as expectation. Then prove that the limit exists and is equal to f(c) for some c. Find c.
Let f(x) be a continuous function on [0, 1] and consider the limit 1 Xj +... f + In · drn. lim dx1 ... ... n00 Give (1) a probabilistic interpretation by interpreting the integration as expectation. Then prove that the limit exists and is equal to f(c) for some c. Find c.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let f(x) be a continuous function on [0, 1] and consider the limit
1
+ In
lim
f
dx1
· drn.
Give (1) a probabilistic interpretation by interpreting the integration as expectation. Then prove
that the limit exists and is equal to f(c) for some c. Find c.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbca55d5a-4c0c-453b-b624-8aa6a89b3c63%2Fc4fdbf7e-75d1-4fad-84cf-297501567e8a%2Fg6e27k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f(x) be a continuous function on [0, 1] and consider the limit
1
+ In
lim
f
dx1
· drn.
Give (1) a probabilistic interpretation by interpreting the integration as expectation. Then prove
that the limit exists and is equal to f(c) for some c. Find c.
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