The random vector T = [X, f] has a uniform joint distribution inside a half of u

Question

The random vector T = [X, f] has a uniform joint distribution inside a half of unit disk as shown in the figure Answer the following questions. (a) Define the joint probability density function (PDF) of X and Y, Sketch the joint PDF in a3-DpIot (b) Obtain the joint cumulative distribution function (d) Obtain and plot the marginal PDFs of X and Y respectively. (e) Obtain the conditional PDF?s Are X and Y statistically independent? Provide the reasoning behind your conclusion. (f) Guess the sign of the correlation coefficient between X and Y, pxy without calculations and provide the reasoning behind your guess. (g) Compute p xy using the probability functions obtained above.

Explanation / Answer

The random vector T = [X, f] has a uniform joint distribution inside a half of u

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