Thread: distribution function

Hi can you help me to solve the following problem?. thank you

Let X1 and X2 denote a random sample of size 2 from a distribution with p.d.f. (densitity function) f(x)=1 , 0<x<1, zero elsewhere. Find the distribution function and p.d.f. of Y=X1/X2

Originally Posted by user

Hi can you help me to solve the following problem?. thank you

Let X1 and X2 denote a random sample of size 2 from a distribution with p.d.f. (densitity function) f(x)=1 , 0<x<1, zero elsewhere. Find the distribution function and p.d.f. of Y=X1/X2

Read these:

Ratio Distribution -- from Wolfram MathWorld

Ratio distribution - Wikipedia, the free encyclopedia

Quotient of two random variables

Hi can you help me to solve the following problem?. But without stochastics theory. I must to use theory of probability and transformations. Thank you

Let X1 and X2 denote a random sample of size 2 from a distribution with p.d.f. (densitity function) f(x)=1 , 0<x<1, zero elsewhere. Find the distribution function and p.d.f. of Y=X1/X2

Originally Posted by user

Hi can you help me to solve the following problem?. But without stochastics theory. I must to use theory of probability and transformations. Thank you

Let X1 and X2 denote a random sample of size 2 from a distribution with p.d.f. (densitity function) f(x)=1 , 0<x<1, zero elsewhere. Find the distribution function and p.d.f. of Y=X1/X2

If you read the links I gave you will know that the distribution of Y/X where X and Y are continuous independent random variables with pdf's f(x) and g(y) respectively is given by

. This is easily proved using the 'Change of variable (transformation)' theorem.

For your problem, note that f(uy) = 1 if and zero otherwise.

Then:

Case 1: h(u) = 0 for u < 0.

Case 2: for .

Case 3: for .