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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...
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- Spring '11
- Probability, Probability distribution, probability density function, probability density