Quiz_7_Solutions

# Quiz_7_Solutions - n with 2 we have this moment generating...

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Quiz #7 – Friday, October 19 th NAME: ______________________________ Grade: __________ out of 25. You have 30 minutes to complete this Quiz. This Quiz is a closed book and Notes exam. You may use the Tables I have distributed in class, though. Exercises 3 and 4 are on the reverse side. Exercise 1: (5 points) I am giving you the moment generating function of X which is a Binomial random variable. Find E(X) using the moment generating function. First find the first derivative of the moment generating function, which is: ( 29 ( 29 1 ' 1 n t t X M t npe pe p - = + - . Evaluate at t=0 and you have E(X)=np(p+1-p) n-1 = np Exercise 2: (5 points) If a random variable Y has the following moment generating function: ( 29 ( 29 2 0.35 0.65 t X M t e = + , name it’s distribution function, and the values of its parameters. Using the moment generating function of Exercise 1, we can see that by replacing p with 0.35 and

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Unformatted text preview: n with 2 we have this moment generating function. Thus Y ~ Bin (2, 0.35) ( 29 ( 29 1 n t X M t pe p = + -Exercise 3: (10 points) If Z~Bin(15,0.4) Find: a) P(X<10) b) ( 29 5 9 P X o < Using the Tables a) ( 29 ( 29 10 9 .966 P X P X < = = mand b) ( 29 ( 29 ( 29 ( 29 ( 29 5 9 9 5 8 4 .905 .217 0.688 P X P X P X P X P X < = <-< =-=-= Exercise 4: (10 points) In a class I have 40 right handed students and 10 left handed students. I select a random sample of 8 students. Let X be the number of right handed students in my sample. a) (5 points) State the distribution of X, by clearly writing all the parameters. b) (5 points) Find P(X=3). a) Hypergeometric with N=50, M=40, n=8 b) ( 29 40 10 3 5 3 50 8 P X = = (This exercise has a flaw… It can be seen in another way… It can be seen as a Binomial with n=8 and p=0.8. Why??)...
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Quiz_7_Solutions - n with 2 we have this moment generating...

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