If X has a gamma(t,n).Find the distribution of cX,c>0 ??

Answered Same DayDec 20, 2021

Answer To: If X has a gamma(t,n).Find the distribution of cX,c>0 ??

Robert answered on Dec 20 2021

119 Votes

Problem
If X has a gamma(t,n).Find the distribution of cX,c>0.
Solution
X ∼ G(t, n). The pdf of X is
f(x) = n
t
Γ(t)x
t−1e−nx, x > 0
Let Y = cX ⇒ X = Yc . Thus
dx
dy =
1
c .
The pdf of Y is
f(y) = f(x)
∣∣dx
dy
∣∣
= n
t
Γ(t) (y/c)
t−1e−n(y/c)
1
c
= (n/c)
t
Γ(t)...

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If X has a gamma(t,n).Find the distribution of cX,c>0 ??

Answer To: If X has a gamma(t,n).Find the distribution of cX,c>0 ??

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