Answer in Statistics and Probability for yoki #204730
October 24th, 2022
If X has uniform distribution over [0,1], find the density function and distribution function of Y D 3X: Identify the distribution of Y
Solution:
“Xsim U[0,1]”
“Y=3Xn\Rightarrow X=dfrac Y3”
“P(Yle r)=P[0le Xle dfrac r3]=dfrac r3” …(i)
As “0<x<1, 0<dfrac Y3<1”
“Rightarrow 0<Y<3”
Now, differentiating (i) to get its PDF.
“f_Y(t)=(dfrac t3)’=dfrac 13”
Thus, distribution function:
“P(Yle r)={dfrac r3, 0<r<3n\ 0, otherwise”
And density function:
“f_Y(t)=dfrac 13;0<t<3n\ 0, otherwise”