Not sure if that's the right answer, but I solved by myself:
1) e^z/6
2) 1
Let đ and đ be independent continuous random variables that are uniformly distributed on (0,1) . Let đť=(đ+2)đ . Find the probability đ(lnđťâĽđ§) where đ§ is a given number that satisfies đ^đ§<2 . Your answer should be a function of đ§ .
1)đ(lnđťâĽđ§)=
2)Let đ be a standard normal random variable, and let đšđ(đĽ) be its CDF. Consider the random variable đ=đšđ(đ) . Find the PDF đđ(đ§) of đ . Note that đđ(đ§) takes values in (0,1) .
đđ(đ§)=
I draw a grap of ln H, but e^z<2, meaning z<ln 2, which does not give any information in terms of lnđťâĽđ§.
Can anyone help solve this?
Thank you
7 answers
a)Any hints...did you integrate from the expression to 1 for both x and y?
your pdf does not integrate to 1
b)1?
your pdf does not integrate to 1
b)1?
I got P(YâĽe^z/x+2) and don't know how to go further. It seems to be getting a function of z and x
From that point, P(YâĽe^z/x+2), you can double integrate, and you result in the integration from 0 to 1 of 1-((e^z)-(x+2)). Therefore the result is:
1-((e^z)*(ln(3)-ln(2)))
resulting in:
1-((e^z)*(ln(3/2)))
1-((e^z)*(ln(3)-ln(2)))
resulting in:
1-((e^z)*(ln(3/2)))
a) 1-((e^z)*(ln(3/2)))
b) 1
b) 1
fz = 1/sqrt(-2*sqrt(z*sqrt(2*pi)))
can anymone confirm ??
can anymone confirm ??
typo, should read: fz = 1/sqrt(-2*ln(z*sqrt(2*pi)))