The probability density function of a random variable X is given by: f(x) = { kx(2 - x), 0 < x < 2 0, e.w. (a) Find the value of k (b) Find the distribution function F(X) (c) Find P(X > 3)
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We know that the total probability should be equal to 1. So, we can write the integral of the probability density function from 0 to 2 and set it equal to 1: $$\int_0^2 kx(2-x) dx = 1$$ Now, let's solve the integral: $$k \int_0^2 (2x - x^2) dx = 1$$ $$k \left[ Show more…
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