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4. (a) A man tosses a fair coin 10 times. Find the probability that he will have: (i) heads on the first five tosses and tails on the next five tosses, (ii) heads on tosses 1,3,5,7,9 and tails on 2,4,6,8,10 tosses, (iii) 5 heads and 5 tails,

4. (a) A man tosses a fair coin 10 times. Find the probability that he will have: (i) heads on the first five tosses and tails on the next five tosses, (ii) heads on tosses 1,3,5,7,9 and tails on 2,4,6,8,10 tosses, (iii) 5 heads and 5 tails,

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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4. (a) A man tosses a fair coin 10 times. Find the probability that he will have: (i) heads on the first five tosses and tails on the next five tosses, heads on tosses 1,3,5,7,9 and tails on 2,4,6,8,10 tosses, (ii) (iii) 5 heads and 5 tails, (iv) at least 5 heads, and (v) not more than 5 heads. (b) Consider a binomial random variable X with parameters n and p. Let Y = X/n be a new random. Show that the expected value of Y is p and the variance of Y is pq/n. If p(y) is the p. m. f. for Y, show that nY~b(n,p). What are the possible values that Y can take on?
Transcribed Image Text:4. (a) A man tosses a fair coin 10 times. Find the probability that he will have: (i) heads on the first five tosses and tails on the next five tosses, heads on tosses 1,3,5,7,9 and tails on 2,4,6,8,10 tosses, (ii) (iii) 5 heads and 5 tails, (iv) at least 5 heads, and (v) not more than 5 heads. (b) Consider a binomial random variable X with parameters n and p. Let Y = X/n be a new random. Show that the expected value of Y is p and the variance of Y is pq/n. If p(y) is the p. m. f. for Y, show that nY~b(n,p). What are the possible values that Y can take on?
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