(10 points) We denote by X the profit (in USD bn) of Microsoft in the third...

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(10 points) We denote by X the profit (in USD bn) of Microsoft in the third quarter of 2023, and by Y the profit (in USD bn) of Apple in the third quarter of 2023. A financial analyst models the joint probability density function of X and Y by f(x, y) = = 113xy if 0 x 3 and 0 y 2, 0 otherwise. (a) (5 points) Show that f(x, y) is a joint probability density function. (b) (5 points) Compute the probability that Microsoft's profit is greater than 2 and Apple's profit is greater than 1. (10 points) We denote by X the profit (in USD bn) of Microsoft in the third quarter of 2023, and by Y the profit (in USD bn) of Apple in the third quarter of 2023. A financial analyst models the joint probability density function of X and Y by f(x, y) = = 113xy if 0 x 3 and 0 y 2, 0 otherwise. (a) (5 points) Show that f(x, y) is a joint probability density function. (b) (5 points) Compute the probability that Microsoft's profit is greater than 2 and Apple's profit is greater than 1.