1. ## continuous random variables

A continuous random variable Y has cdf

F(y) = a + ay / 2, − 2 < y < 0
1− becy 3 , y > 0
(a)
Sketch the cdf when a = 1/2, b = 1/2 and c = 1.
Then derive Y's pdf generally, and sketch it when a = 1/2, b = 1/2 and c = 1.
Finally, write down the range of possible values for a, b and c.

(b) Find P(Y > −1| Y < 1) when a = 1/2, b = 1/2 and c = 1.

2. Originally Posted by Mathew
A continuous random variable Y has cdf

F(y) = a + ay / 2, − 2 < y < 0
1− becy 3 , y > 0 Mr F says: The formatting of this is horrible. I can't understand it.

(a)
Sketch the cdf when a = 1/2, b = 1/2 and c = 1.
Then derive Y's pdf generally, and sketch it when a = 1/2, b = 1/2 and c = 1.
Finally, write down the range of possible values for a, b and c.

(b) Find P(Y > −1| Y < 1) when a = 1/2, b = 1/2 and c = 1.

Where are you stuck? Note:

(a) Differentiate the cdf to get the pdf.

(b) $\Pr(Y > -1 | Y < 1) = \frac{\Pr(-1 < Y < 1)}{\Pr(Y < 1)} = \frac{F(1) - F(-1)}{F(1)}$.