A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows. f(x) = kx^2 0 ? x ? 2
0 otherwise
(a) Find the value of k.
(b) What is the probability that the lecture ends within 1 min of the end of the hour?
c) What is the probability that the lecture continues beyond the hour for between 15 and 45 sec?
(d) What is the probability that the lecture continues for at least 75 sec beyond the end of the hour?

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step-by-step explanation:

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).

step-by-step explanation:

rectangles are made up of 4 right angles, which means that a side and a base meet perpendicular to one another.   their slopes then have to reflect perpendicular slopes.   perpendicular slopes are opposite reciprocals of one another.   for example, if the slope of one line is +2/3, then the perpendicular slope to that would be -3/2.   so we look for that combination in our choices.

all of them satisfy that condition (so what's the question, i guess? )