Let p be the probability of obtaining heads when a coin is tossed and assume that p is in the range of 0.4 to 0.6. Suppose we toss the coin N times and form an estimate of p as NH N where NH is the number of heads showing up in N tosses. Is p sample mean? Explain whether p is biased or not. Find Var{p}. (a) (b) Show that the variance of p is upper bounded as Var{p} < 0.25/N. Find the smallest value of N such that P||p – pl 2 0.01p] < 0.1. (c) (d)
Let p be the probability of obtaining heads when a coin is tossed and assume that p is in the range of 0.4 to 0.6. Suppose we toss the coin N times and form an estimate of p as NH N where NH is the number of heads showing up in N tosses. Is p sample mean? Explain whether p is biased or not. Find Var{p}. (a) (b) Show that the variance of p is upper bounded as Var{p} < 0.25/N. Find the smallest value of N such that P||p – pl 2 0.01p] < 0.1. (c) (d)
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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![Let p be the probability of obtaining heads when a coin is tossed and assume that p
is in the range of 0.4 to 0.6. Suppose we toss the coin N times and form an estimate of p as
1.
NH
N
where NH is the number of heads showing up in N tosses.
Is p sample mean? Explain whether p is biased or not.
Find Var{p}.
(a)
(b)
(c)
Show that the variance of p is upper bounded as Var{p} < 0.25/N.
(d)
Find the smallest value of N such that P||p – p| 2 0.01p] < 0.1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c0c65b8-afb7-4ed4-8c00-d498284fe5d7%2F49fb9e0d-56f3-485b-af75-a05f83068508%2Fknjnj5g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let p be the probability of obtaining heads when a coin is tossed and assume that p
is in the range of 0.4 to 0.6. Suppose we toss the coin N times and form an estimate of p as
1.
NH
N
where NH is the number of heads showing up in N tosses.
Is p sample mean? Explain whether p is biased or not.
Find Var{p}.
(a)
(b)
(c)
Show that the variance of p is upper bounded as Var{p} < 0.25/N.
(d)
Find the smallest value of N such that P||p – p| 2 0.01p] < 0.1.
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