14.4.2. Conditional PDF

Try these first

1. 1.

   Define Conditional PDF in your own words.

   Hint

   Think about how one variable's understanding depends on another.

2. 2.

   What is the formula for Conditional PDF?

   Hint

   Recall the relationship between joint and marginal PDFs.

3. 3.

   What is the formula for Conditional PDF?

   • f_{X,Y}(x,y) / f_Y(y)
   • f_Y(y) / f_{X,Y}(x,y)
   • f_{X,Y}(x,y) + f_Y(y)

   Hint

   Consider the relationship defined by ratios.

4. 4.

   True or False: Conditional PDF can be interpreted as the ratio of joint PDF to marginal PDF.

   • True
   • False

   Hint

   Remember the definition of Conditional PDFs.

5. 5.

   Given two independent random variables X and Y, explain how their independence affects their conditional densities.

   Hint

   Think about the implications of independence in probability.

6. 6.

   A random variable has a joint PDF defined by f_{X,Y}(x,y) = 3x^2y for 0 < x < 1 and 0 < y < 1. Calculate the Conditional PDF f_{X|Y}(x|y).

   Hint

   Start by finding the marginal function before approaching the conditional PDF.