A random variable has distribution function F(z) = P(y<= z) given by (this is a piecewise function)
0 if z < -1
1/2 if -1 <= z < 1
1/2 + 1/4(z-1 if 1 <= z < 2
1 if 2 <= z
What is P(Y = 2)?
Find all the numbers t with the property that both P(Y <= t) >= 1/2 and P(Y >= t) >= 1/2
The Attempt at a Solution
For the P(Y=2) I integrated at the point 2 plus and minus epsilon and came up with 1/4z - 0 where z =2. Thus, 1/2. My concern is that this problem has a lot of constants Thus, I would expect P(Y=x) to equal 0 everywhere but in [1,2). Then I have no idea how to find the median of the distribution function. Sorry, if these are easy questions. The class is being taught without a book and I'm afraid I'm not used to that.