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In: Statistics and Probability

The joint probability density function for two continuous random variables ?? and ?? is ??(??, ??)...

The joint probability density function for two continuous random variables ?? and ?? is
??(??, ??) = ??(3??2 − ??), 0 < ?? < 1, 0 < ?? < 1.
Answer the following:
(a) Find the value of ?? such that ??(??, ??) is a valid probability density function.
(b) Find the marginal probability density function for ??, ??(??).
(c) Find the marginal probability density function for ??, ??(??).
(d) Find the conditional probability density function for ??|?? = ??, ??(??|??).
(e) Based on your answers from (b) to (d) only, are ?? and ?? independent?
(f) Calculate the covariance between ?? and �

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orchestra answered 2 years ago
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