Let X₁, Xn be independently and identically distributed Beta (a, b) random variables where a >o and b>0 are finite constants. The mean and varian for Beta (a, b) distribution is ab and respectively. (a+b)²(a+b+l) Xi a atb Let Xn for în lim |=| using the definition convergence in propability, show that а atb (Def. for convergence: Xn = пях ) X: for any P{1xn-x1 < €} = 1 or for any € > 0,
Let X₁, Xn be independently and identically distributed Beta (a, b) random variables where a >o and b>0 are finite constants. The mean and varian for Beta (a, b) distribution is ab and respectively. (a+b)²(a+b+l) Xi a atb Let Xn for în lim |=| using the definition convergence in propability, show that а atb (Def. for convergence: Xn = пях ) X: for any P{1xn-x1 < €} = 1 or for any € > 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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Transcribed Image Text:Let X₁, Xn be independently and identically
distributed Beta (a, b) random variables where
a >o and b>0 are finite constants. The mean
and varian for Beta (a, b) distribution is
ab
and
, respectively
(a+b)2(a+b+1)
Xi
a
atb
Let Xn
JJ
|=|
using the definition
for convergence in probability, show that
Xn
а
atb
(Def. for convergence: Xn
2x: for any e > 0,
lim
msos P{1xn-x1<€} =) or for any
€ 30, lim P{ |X₁-X1> 6} = 0 )
x
nga
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