How can I show that the product of two cdfs also have the properties of a cdf?
Multiplying Cumulative Distribution Functions
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probability
probability-distributions
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1Hint: The product of two cdfs is indeed a cdf. However, the analogous statement for pdfs doesn't hold. Consider the pdf of $ Exp(1) $ and the pdf of $ U(0,1) $. – 2017-01-21
1 Answers
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In short, yes. We want to show that $F(x)G(x)$ is continuous from the right, and non-decreasing, both of which can follow from the definitions and are easy to verify.
And good luck with the homework. Don't forget to print out a copy as well :)