{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Midterm2

# Midterm2 - Mathematics Department UCLA T Richthammer spring...

This preview shows pages 1–2. Sign up to view the full content.

Mathematics Department, UCLA T. Richthammer spring 09, midterm 2 May 18, 2009 Midterm 2: Math 170B Probability, Sec. 1 1. Let X, Y be continuous RVs. (a) What is the conceptual diﬀerence between E ( X | Y = y ) and E ( X | Y )? (b) Give the deﬁnition of E ( X | Y ) and show that E ( E ( X | Y )) = E ( X ). Answer: (a) E ( X | Y = y ) is a number for every choice of y , whereas E ( X | Y ) is a function of Y and thus a RV (which has certain values with certain probabilities). (b) We have E ( X | Y ) = h ( Y ), where h ( y ) = E ( X | Y = y ) = R xf X ( x | Y = y ) dx = R x f X,Y ( x,y ) f Y ( y ) dx . So E ( E ( X | Y )) = E ( h ( Y )) = R h ( y ) f Y ( y ) dy = R ( R x f X,Y ( x,y ) f Y ( y ) dx ) f Y ( y ) dy = R xf X,Y ( x, y ) dxdy = E ( X ). 2. You order an item at time 0. It takes a random time T until the item is delivered. At a random time X between 0 and T you get an email conﬁrming your order. Suppose that T is a RV with E ( T ) = 6 and V ( T ) = 3. Calculate the expectation and variance of the time X you get the conﬁrmation email in the two cases (a) and (b). (a) Assume that

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Midterm2 - Mathematics Department UCLA T Richthammer spring...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online