Q. 1 (i) Find moment generating functions (mgf) of the following probability distributions. (ii) Using mgf found in (i) above, find mean and variance. (i) fx(x;n,p) = {x)p*q"=*;_x= 0,1,2,-, n, 0; е. w. (e-^a*. x = 0,1,2,, (ii) fx(x; 2) = 0; x! е. w. 1 (iii) fx(x; a, ß) : r(@)gax«=?e¬x/B; 0 < x< ∞ (iv) fx(x; ß) = e-*/B;0 < x< ∞ (v) fx (x; µ, o) = exp[- (x-µ)²] 1 exp - еxp ;-00

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Q. 1 (i) Find moment generating functions (mgf) of the following
probability distributions.
(ii) Using mgf found in (i) above, find mean and variance.
(i) fx(x;n,p) = {x)p*q"=*;_x= 0,1,2,-, n,
0;
е. w.
(e-^ax.
x = 0,1,2,,
(ii) fx(x; 2) =
0;
x!
е. W.
1
( ii) fx (x; α, β) :
r(a)ga x“-te¬x/B; 0 < x <∞
(iv) fx(x; ß) = e-x/B;0 < x< ∞
1
(x-µ)²]
(v) fx(x; µ, o) = To
VER exp[-
;-00 < x< ∞
2σ2
1
( vi) fK (x; α, β)
B(a,f) *"-(1 – x)*-1; 0 < x < 1
%3D
Г(а)Г(В)
where B(a,ß) =
r(a+B)
(vii) F<(x, a, f) = x«-lexp[-;)"]:0<xs ∞
еxp
Please present all results in a table.
Transcribed Image Text:Q. 1 (i) Find moment generating functions (mgf) of the following probability distributions. (ii) Using mgf found in (i) above, find mean and variance. (i) fx(x;n,p) = {x)p*q"=*;_x= 0,1,2,-, n, 0; е. w. (e-^ax. x = 0,1,2,, (ii) fx(x; 2) = 0; x! е. W. 1 ( ii) fx (x; α, β) : r(a)ga x“-te¬x/B; 0 < x <∞ (iv) fx(x; ß) = e-x/B;0 < x< ∞ 1 (x-µ)²] (v) fx(x; µ, o) = To VER exp[- ;-00 < x< ∞ 2σ2 1 ( vi) fK (x; α, β) B(a,f) *"-(1 – x)*-1; 0 < x < 1 %3D Г(а)Г(В) where B(a,ß) = r(a+B) (vii) F<(x, a, f) = x«-lexp[-;)"]:0<xs ∞ еxp Please present all results in a table.
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