a1su112131

# a1su112131 - 1(b(5 marks Let X 1,X 2 be i.i.d r.v.’s with...

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

MATH 2131 3.00 MS2 Assignment 1 Total marks = 40 Question 1: Let ( X,Y ) have the joint probability density function f X,Y ( x,y ) = ( cx/y 2 , y - 1 < x < y, 1 < y < 2 , 0 , otherwise. (a) (4 marks). Find c such that f X,Y ( x,y ) is a joint probability density function. (b) (4 marks). Find f X ( x ). (c) (4 marks). Find P ( X > 1 ,Y < 2). Question 2: A university club consists of 4 men and 6 women. Two members are chosen at random without replacement. Let X = ( 0 , if ﬁrst person chosen is male, 1 , if ﬁrst person chosen is female, Y = ( 0 , if second person chosen is male, 1 , if second person chosen is female. (a) (4 marks). Find p X,Y ( x,y ). (b) (2 marks). Find p Y ( y ). Question 3: (a) (5 marks). Two fair dice are rolled. Let r.v.’s X and Y denote the number of dots showing on the ﬁrst and second dice, respectively. Show that X and Y are independent if their joint probability distribution function is given by p X,Y ( x,y ) = ( 1 / 36 , x = 1 , 2 ,..., 6; y = 1 , 2 ,..., 6 , 0 , otherwise.

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: 1 (b) (5 marks). Let X 1 ,X 2 be i.i.d. r.v.’s with common probability density function f ( x ) = ( e-x , x > , , otherwise. Find P ( X 1 + X 2 > 2) . Question 4: Let ( X,Y ) have the joint probability distribution function f X,Y ( x,y ) = ( (6-x-y ) / 8 , < x < 2 , 2 < y < 4 , , otherwise. (a) (5 marks). Find f Y | X ( y | x ). (b) (3 marks). Find P (2 < Y < 3 | X = 1) . Question 5: (4 marks). The opening market prices per bushel for corn and wheat are known to independently each follow the probability distribution function f ( x ) = ( e-( x-5) , x ≥ 5 . , otherwise. An investor decides she will buy whichever commodity has the lower price. Find the probability density function for the price per bushel that the investor will have to pay. 2...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

a1su112131 - 1(b(5 marks Let X 1,X 2 be i.i.d r.v.’s with...

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

View Full Document
Ask a homework question - tutors are online