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3 cards from this section. Quick, good the night before a test.
What is a joint probability density function?
Think about how we measure the partnership of two events.
How do we derive a marginal distribution?
Consider what happens when you ignore one of the variables.
What does the joint pdf represent?
Think about the definition of joint probabilities.
True or False: Marginal distributions can be obtained from joint distributions.
Consider how you isolate one variable from the others.
Given two independent random variables with joint distribution defined as f(x,y) = 2xy for 0 < x < 1 and 0 < y < 1, find the marginal distributions, and verify their independence.
Use integration for marginals and confirm through multiplicative property.
A random variable Z is defined as Z = X + Y, where X and Y are independent uniform random variables on [0, 1]. Determine the distribution of Z using joint distributions.
Consider how to apply convolution for deriving the distribution.
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