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

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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
Transcribed Image Text: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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