# Lab4 - Statistics 103 Lab 4 LAB PROBLEMS 1 Book problem...

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Statistics 103: Lab 4 LAB PROBLEMS 1. Book problem 8.3 (This one is a bit tricky. You can assume the two students are chosen with replace- ment. Hint: use the Binomial PMF to ﬁgure out the marginals; ﬁgure out which entries of the joint PMF are zero; then ﬁll in the rest). 2. Book problem 8.10. 3. Book problem 8.14. 4. Suppose X and Y are independent random vari- ables with E ( X ) = μ 1 , var ( X ) = σ 2 1 , E ( Y ) = μ 2 , and var ( Y ) = σ 2 2 . Compute E (2 X - 0 . 1 Y + 5), E ( μ 1 X + σ 2 2 Y + μ 2 ), var ( - 3 Y + μ 2 X + 999), SD (5 X - 14 Y ). PRACTICE PROBLEMS 1. Let us assume that X 1 ,X 2 ,X 3 ,...,X n are indepen- dent normal random variables mean μ and variance σ 2 . That is, X i N ( μ,σ 2 ) for i = 1 , 2 , 3 ,...,n . Let Y = n i =1 X i . Find EY , E ( ¯ X ), E ( Y - n ¯ X ), var ( Y ), var ( ¯ X ), var ( Y - n ¯ X ), var ( μ + σ 2 ), Distribution of Y , Dis- tribution of ¯ X . For var ( Y - n ¯ X ), simplify Y - n ¯ X ﬁrst before solving the question. 2. Suppose that you have a box which contains cards. Each card has either “0” or “1” is written on it. Suppose further that when drawing a card at ran- dom, the probability that you see “1” on it is p . Now randomly draw n cards with replacement and let X 1 ,X 2 ,...,X n denote the n card numbers. Then, we say that X i has a Binomial distribution based on 1 trial with probability of success p , writ- ten X i Bin (1 ,p ). Now, consider Y = n i =1 X i . Then,

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Lab4 - Statistics 103 Lab 4 LAB PROBLEMS 1 Book problem...

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