6. Let P be the standard normal distribution, i.e., P is the proba- bility measure on (R, B(R)) given by 1 dP(x) = 를 = e dx. √2πT Consider the random variables 21 fn(x) = (1 + x²) en+2, x Є R, n Є N. Using the dominated convergence theorem, prove that the limit Total marks 9 exists and find it. lim E(fn) n∞ [9 Marks]
6. Let P be the standard normal distribution, i.e., P is the proba- bility measure on (R, B(R)) given by 1 dP(x) = 를 = e dx. √2πT Consider the random variables 21 fn(x) = (1 + x²) en+2, x Є R, n Є N. Using the dominated convergence theorem, prove that the limit Total marks 9 exists and find it. lim E(fn) n∞ [9 Marks]
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Question
![6.
Let P be the standard normal distribution, i.e., P is the proba-
bility measure on (R, B(R)) given by
1
dP(x) =
를
=
e dx.
√2πT
Consider the random variables
21
fn(x) = (1 + x²) en+2,
x Є R, n Є N.
Using the dominated convergence theorem, prove that the limit
Total marks 9
exists and find it.
lim E(fn)
n∞
[9 Marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd66c7573-6777-48ff-9bfb-9b3df1a769a6%2F810e5105-1854-4275-adda-8d3518fa6dda%2Fkavdxbm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6.
Let P be the standard normal distribution, i.e., P is the proba-
bility measure on (R, B(R)) given by
1
dP(x) =
를
=
e dx.
√2πT
Consider the random variables
21
fn(x) = (1 + x²) en+2,
x Є R, n Є N.
Using the dominated convergence theorem, prove that the limit
Total marks 9
exists and find it.
lim E(fn)
n∞
[9 Marks]
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