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just need some help with number 5 Suppose that the time at which a businessperson leaves...

just need some help with number 5

Suppose that the time at which a businessperson leaves for lunch (in hours after noon) is a continuous random variable X with probability density function f(x) = c(1-x)2 for 0 < x < 1, where c is the appropriate constant, and f(x) = 0 otherwise.
1.Determine the value of c for this to be a legitimate pdf.
2.Sketch this pdf. (Hand-drawn is fine.)
3.Determine the probability that this businessperson leaves for lunch before 12:15. Also shade the region corresponding to this probability in your pdf sketch.
4.Determine the probability that this businessperson leaves for lunch at exactly 12:15.
5.Suppose that you notice that this businessperson has not yet left for lunch by 12:30. Determine the (conditional) probability that he/she will leave before 12:45, given that he/she has not left by 12:30.

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Answer #1

As per CheggpOlicy we ar able to write first 4 parts.

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