{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

a3su112131 (1)

# a3su112131 (1) - In a ﬁve-game playo± series between...

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

MATH 2131 3.00 MS2 Assignment 3 Total marks = 50 Question 1: Let ( X,Y ) have the joint pdf f X,Y ( x,y ) = ( e - y , 0 < x < y < , 0 , otherwise. (a) (4 marks). Find E ( XY ). (b) (6 marks). Find Cov( X,Y ). (c) (4 marks). Find ρ X,Y . Question 2: Let X 1 ,...,X n be a random sample on r.v. X whose mean is μ and variance is σ 2 . Let ¯ X = n i =1 X i /n and S 2 = n i =1 ( X i - ¯ X ) 2 / ( n - 1). Show that (a) (2 marks). E ( ¯ X ) = μ . (b) (2 marks). Var( ¯ X ) = σ 2 /n . (c) (5 marks). E ( S 2 ) = σ 2 . Question 3: (3 marks). The number of transactions handled by a bank teller in a day is a r.v. X with a mean of 80 and a standard deviation of 5. Using Chebyshev’s inequality, what can be said about the probability that the teller will handle between 70 and 90 transactions in a day? Question 4: (4 marks). Assume that the number of games, X , that a baseball relief pitcher will save in n games follows a binomial distribution, i.e., X Binomial( n,p

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.

Unformatted text preview: ). In a ﬁve-game playo± series between equally matched teams, the number of games played is a r.v., N , with pmf p N ( n ) = ( ± n-1 2 )± 1 2 ) n-1 , n = 3 , 4 , 5 , otherwise. Find the expected number of saves this relief pitcher will make in this series. 1 Question 5: (3 marks). If X and Y are r.v.’s with equal variances, ﬁnd Cov( X + Y,X-Y ). Question 6: (6 marks). Let X , Y , and Z be uncorrelated r.v.’s with variances σ 2 X , σ 2 Y , and σ 2 Z , respectively. Let U = Z + X and V = Z + Y . Find ρ U,V . Question 7: Let (X,Y) have the joint pdf f X,Y ( x,y ) = ( 8 xy, < x < y < 1 , , otherwise. (a) (7 marks). Find E ( X | Y = y ) and Var( X | Y = y ). (b) (4 marks). Find the pdf of r.v. E ( X | Y ). 2...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

a3su112131 (1) - In a ﬁve-game playo± series between...

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

View Full Document
Ask a homework question - tutors are online