Description

1 Definitions
1. The pdf of an exponential distribution is given by
pX(x) = e−xu(x)
where u(·) is the unit step function.
2 Problems
1. Find FX(x).
2. Let X and Y be iid exponential. Find FXY (z,z) 3. Show that (1.1.1)
= − e
2 4. Find
Pr(Y ≤ z, X ≤ Y)
5. Let (2.4.1)
Z = max(X,Y)
Show that (2.5.1)
FZ(z) = Pr(X ≤ z, X > Y) + Pr(Y ≤ z, X ≤ Y)
6. Find the pdf of Z.
7. Find the pdf of W = min(X,Y).
8. Find FW(vZ), where v is a constant.
9. Find E [FW(vZ)].
10. Find the pdf of V = WZ . (2.5.2)
Pr(X ≤ z, XpX,Y(x,y)dxdy (2.3.1)
−∞ −∞
e
− (2.3.2)