ec41f10MT2_sol (1)

# ec41f10MT2_sol (1) - Kata Bognar [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */ Economics...

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Kata Bognar [email protected] Economics 41 Statistics for Economists UCLA Fall 2010 Midterm 2 - suggested solutions by Minji Kang - Part I - Multiple Choice Questions (4 points each) 1. Chebyshev’s theorem is applicable to: B (a) bell-shaped distributions only (b) any kind of distribution (c) continuous distributions only (d) discrete distributions only 2. A professor responds to student questions by email. The following table describes the number of emails that the professor may receive from the students each day. number of emails probability 0 0.05 1 0.1 2 0.2 3 0.25 4 0.3 5 0.1 It takes the professor 10 minutes to respond each email. How much time should the professor expect to spend responding emails per day? C (a) 9.5 (b) 2.95 (c) 29.5 (d) none of the above Explanation: Denote by X the number of emails the professor receives per day. Then E [ X ] = 0(0 . 05)+1(0 . 1)+2(0 . 2)+3(0 . 25)+4(0 . 3)+5(0 . 1) = 2 . 95 . Since answering an email takes 10 minutes, the expected time the professor spends with responding to emails is E [10 X ] = 10 E [ X ] = 29 . 5 . 3. The American Veterinary association claims that the annual costs of medical care for dogs has a mean of \$100 and a variance of 30, while the annual costs of medical care for cats has a mean of \$120 and a variance of 35. Suppose that a person has a cat and a dog and no other pets. Also assume that the need for medical care for the dog and for the cat is independent. Then this person D (a) expects to spend \$220 on medical care for his/her pets with a variance of 75. (b) expects to spend \$120 on medical care for his/her pets with a variance of 30. (c) expects to spend \$100 on medical care for his/her pets with a variance of 30. (d) none of the above is true Explanation: Denote by X the annual cost of medical care for a dog and by Y the annual cost of medical care for a cat. Then the total costs of medical care for both pets is X + Y. It is given that E [ X ] = 100 ,E [ Y ] = 120 ,V ar [ X ] = 30 and V ar [ Y ] = 35 . Using the formulas E [ X + Y ] = E [ X ] + E [ Y ] and V ar [ X + Y ] = V ar [ X ] + V ar [ Y ] , one gets that the expected value of total medical costs is \$220 with a variance of 65. 1

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4. The maximum likelihood estimate is C (a) a random variable (b) a function of random variables (c) a value of a statistic (d) a statistic Explanation: See deﬁnitions in the book / slides. 5. X is a random variable with a p.d.f f ( x ) = a (3 - x ) for 1 < x < 3 where a is a constant. Then the expected value of X is B (a) 1/2 (b) 5/3 (c) 1 (d) none of the above Explanation: Since f ( x ) is a density function, R 3 1 a (3 - x )d x = 1 . This implies that a = 1 2 . Then E [ X ] = R 3 1 x 1 2 (3 - x )d x = 5 3 . 6. Determine whether the following random variable has a binomial distribution. If not, state the
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## This note was uploaded on 12/28/2010 for the course ECON 41 taught by Professor Guggenberger during the Fall '07 term at UCLA.

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ec41f10MT2_sol (1) - Kata Bognar [email protected] Economics...

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