# Exponential Distribution with Probability

1. Dec 7, 2013

$$f(y) = \begin{cases} 0& \text{for }y< 0,\\ 2y& \text{for }0 ≤ y ≤ .5,\\ 6-6y& \text{for }0.5 < y ≤ 1, \\0& \text{for } y > 1\end{cases}$$

(1) Find cumulative distribution function, F(y)
$$F(y) = \begin{cases} 0& \text{for }y< 0, \\\int_0^y 2t dt = y^2 & \text{for } 0 ≤ y ≤ .5,\\.5^2+ \int_{0.5}^y (6-6t) dt = 6y-3y^2-2 & \text{for }0.5 < y ≤ 1\ \\1& \text{for } y > 1\end{cases}$$

(2) P(1/4 < Y < 3/4) = 6(3/4)-3(3/4)^2-2-(1/4)^2 = 3/4

Could anyone check (1) and (2) for me?

Last edited: Dec 7, 2013
2. Dec 7, 2013