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hw3 - Stat 503 Homework#3 Due in class 9/16(80pts 1(9pts...

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Stat 503 Homework #3 Due in class 9/16 (80pts) 1.(9pts) Consider the population of tossing a die. The random variable Y is defined as following: 1, when get a even number Y= 0, when get a odd number (a) (3 pts) What type of the random variable is Y? (b) (3 pts) Calculate E(Y) (c) (3 pts) Calculate Var(Y) 2. (16 pts) Suppose we toss two dies, let X1 and X2 be the numbers of each toss. (a) (4pts) What is the Pr(X1+X2<5) (b) (4pts) What is the Pr(X1-X2<5) (c) (4pts) What is the E(2X1-X2) (d) (4pts) What is the σ (2X1-X2) 3.(15) In the united States, 42% of the population has type A blood. Consider taking a sample of size 4. let Y denote the number of persons in the sample with type A blood. Find (a) (3 pts) Pr{Y=0} (b) (3 pts) Pr{Y=1} (c) (3 pts) Pr{Y=2} (d) (3 pts) Pr{0≤Y≤2} (e) (3 pts) Pr{0<Y≤2} 4. (8pts) A certain drug causes kidney damage in 1% of patients. Suppose the drug is to be tested on 50 patients. Find the probability that (a) (4pts)none of the patients will experience kidney damage.
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