Question: Please ASAP! For its admission to the Ph.D. program, a university uses two exams, math and physics. In the population of the university applicants, math

Please ASAP!

For its admission to the Ph.D. program, a university uses two exams, math and physics. In the population of the university applicants, math exam score M is distributed according to some continuous CDF F, and physics exam score P is distributed according to somecontinuous CDF G. Moreover, the scores are independent. The university admits a student depending on his or her weighted average percentile across the two exams. Specifically, if x is a student's math exam percentile, and y is a student's physics exam percentile, then the university admits this student if and only if (2/3)*x+(1/3)*y>2/3. What is the probability that a random applicant will be admitted to the Ph.D. program?

Note: a percentile of a given student on an exam is a fraction of students who scored below him or her on the exam. In our setting, it is just the probability that a random student will have a lower score than a given student.

Hint: think what must be the distribution of percentile of a random applicant for each exam?

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