At Starfleet Academy, engineering students must all take the pass/fail course Wa

Question

At Starfleet Academy, engineering students must all take the pass/fail course Warp Drive Mechanics. The probability is 0.65 that a student will pass on the fist try; if they fail the course they can retake it once, with probability .90 that they will pass on the second try, they failed both times and have to change majors while y=1 mean that they passed A) Work out the joint probability mass function Pxy, Give your result as a table and confirm your PMF is formalized B) Calculate the marginal PMF Py C) Calculate the expected number of times a student takes the course?

Explanation / Answer

At Starfleet Academy, engineering students must all take the pass/fail course Warp Drive Mechanics. The probability is 0.65 that a student will pass on the fist try; if they fail the course they can retake it once, with probability .90 that they will pass on the second try, they failed both times and have to change majors while y=1 mean that they passed A) Work out the joint probability mass function Pxy, Give your result as a table and confirm your PMF is formalized B) Calculate the marginal PMF Py C) Calculate the expected number of times a student takes the course?

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