HW2 solution

HW2 solution - PGE337 Introduction to Geostatistics...

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PGE337 Introduction to Geostatistics Homework #2 solution key Question 1 (10 pts) a) When P ( A ) 1/3 , P ( B ) 1/2 and P ( A B ) 3/4 , what is i. 1 1 3 1 ( ) ( ) ( ) ( ) 3 2 4 12 P A B P A P B P A B ii. 1 11 ( ) 1 ( ) 1 12 12 CC P A B P A B     b) Suppose the events D 1 and D 2 are two rare data events (mutually exclusive) in the modeling of a porosity field P ( D 1 ) 10 6 and P ( D 2 ) 10 6 . i. What is the probability that at least one of the events occurs? 6 6 6 12 ( ) 10 10 2 10 P D D   ii. What is the probability that both events occur? ( ) 0 P D D  c) An experiment has only two outcomes. The first has probability p to occur, the second probability p 2 . What is p ? 2 2 {1,2} (1) , (2) ( 1 (2) 1 1 1 4 1 5 22 P p P p P P P pp p          p cannot be negative Question 2 (20 pts) a) Let X be a continuous RV with probability density function f ( x ) 3 4 for 0 x 1 1 4 for 2 x 3 0 elsewhere

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i. Draw the graph of f . ii. Determine the distribution function F of X , and draw its graph. 3 ( ) 0 1 4 11 ( ) 2 3 44 F x x for x F x x for x
b) The distribution function of a RV X is given: F ( x ) 0 x 0 x 2 0 x 1 2 3 1 x 2 11 12 2 x 3 1 3 x i. Plot this distribution function ii. What is P X 1 2 ?

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HW2 solution - PGE337 Introduction to Geostatistics...

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