Question

We denote by X the profit (in USD bn) of Amazon in the first quarter of...

We denote by X the profit (in USD bn) of Amazon in the first quarter of 2020 and by Y the profit (in USD bn) of Facebook in the first quarter of 2020. A financial analyst models the joint probability density function of X and Y by f(x, y) = ( 1 36 (x + y) if 3 ≤ x ≤ 5 and 4 ≤ y ≤ 6, 0 otherwise.

(a) [2 points] Compute:

i. the probability that Amazon’s profit is greater than 4 and Facebook’s profit is greater than 5,

ii. the probability that Amazon’s profit is greater than 4 and Facebook’s profit is smaller than 5.

(b) What is the probability that Amazon’s profit is greater than 2 and Facebook’s profit is greater than 4?

(c) Find a number k such that the probability that Facebook’s profit is greater than k equals 19/36

Math   Calculus   
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