urgent please help!

Question

Randomly select a point on the triangular region whose vertices are (0, 0), (0, 40) and (100, 0). Let the continuous random variable X denote the x-coordinate of the point. Find the cumulative distribution function, the probability density function, and the mean for this random variable.

Answer 1

The region is a right triangle below the line with intercepts at y = 40 and x = 100:

y(x) = 40 - 0.4x

The total area of that triangle is (1/2)(100)(40) = 2000.

CDF(x) = (1/2000).(area from 0 to x) = (1/2000) ∫ y(x) dx, the integral is from 0 to x

PDF(x) = (1/2000) . y(x)

Mean of x = ∫ x . PDF(x) dx, the integral is from 0 to 100.

I assume that you know how to take basic integrals so I left those for you.