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# PSet1 - Problem Set 1 Introduction to Econometrics Fall...

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Problem Set 1 Introduction to Econometrics - Fall 2006 Due Date: Thursday, September 21st, BEFORE CLASS. Each student is responsible for handing one handwritten solution. If working in groups, indicate the members of the group (to facilitate grading). PLEASE SHOW YOUR WORK . 1. The random variable X is distributed normally with N ¡ µ X , σ 2 X ¢ (a) What is the Pr( X µ X ) ? What is the Pr( X µ X + 1 . 96 σ X ) ? (b) Let Y = X µ X σ X . Show that Y is distributed normally with N (0 , 1) ; that is E ( Y ) = 0 and V ar ( Y ) = 1 . (c) Show that E ¡ Y 2 ¢ = 1 2. Let the random variable X be the temperature in Madison, WI at 12:00pm on September 21th. You know that X is distributed normally with N (72 , 100) . (a) What is the probability the temperature is lower than 46 F ? What is the probability the temperature is higher than 90 F ? What is the probability the temperature is in between 65 F and 80 F ? Higher than 80 F ? (b) What is the temperature below which we are not going to fall in 99% of cases?

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