X hasdistribution ona Uni forThe Integer 0,1, 2,3.. n and Y has adiscrete Uni form distribution ondiscrete1,2,3,00show thatVar (x)-Var(Y) = (2nt1)%3D12Let n,L,P) be a probability space and HELwith P(H)>O. Forand defineany arbitrarySubset, A EL,P (A) = P(A\H) = P(An H)PCH)Then Show that (H, LA, P is%3Da spaceprobabilitySupposea fair Coin is flipped twice LetA,"Head on 1st Toss"%3DAz:A, = "Hend on 2 Toss""HeadAz=" Exactly One ttead )%3DShow that A, Az, Ag are Pais wise independent6ut not mutually indapandent

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D x has the Integer 0,1, 2,3...n and Y has discrete show that a discrete Unifor distri butiin on distributin on a Uniform distribtion on 1,2,3,..n Var (x)-Var(y)= (2nt1) %3D 12

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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Question

X has
distribution on
a Uni for
The Integer 0,1, 2,3.. n and Y has a
discrete Uni form distribution on
discrete
1,2,3,00
show that
Var (x)-Var(Y) = (2nt1)
%3D
12
Let n,L,P) be a probability space and HEL
with P(H)>O. For
and define
any arbitrary
Subset, A EL,
P (A) = P(A\H) = P(An H)
PCH)
Then Show that (H, LA, P is
%3D
a space
probability
Suppose
a fair Coin is flipped twice Let
A,
"Head on 1st Toss"
%3D
Az:
A, = "Hend on 2 Toss"
"Head
Az=" Exactly One ttead )
%3D
Show that A, Az, Ag are Pais wise independent
6ut not mutually indapandent

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