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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,

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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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
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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