Show that the most probable number of heads in n tosses of a coin is ;n for even n [that is, f(x) in (7.1) has its largest value for x = n/2] and that for odd n, there are two equal “largest" values of f(x), namely for x = (n + 1) and x = (n – 1). Hint: Simplify the fraction f (x + 1)/ƒ(x), and then find the values of x for which it is greater than 1 [that is, f(x + 1) > f(x)], and less than or equal to 1 [that is, f (x + 1) < f(x)]. Remember that x must be an integer. 10.
Show that the most probable number of heads in n tosses of a coin is ;n for even n [that is, f(x) in (7.1) has its largest value for x = n/2] and that for odd n, there are two equal “largest" values of f(x), namely for x = (n + 1) and x = (n – 1). Hint: Simplify the fraction f (x + 1)/ƒ(x), and then find the values of x for which it is greater than 1 [that is, f(x + 1) > f(x)], and less than or equal to 1 [that is, f (x + 1) < f(x)]. Remember that x must be an integer. 10.
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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![Show that the most probable number of heads in n tosses of a coin is ;n for even n
[that is, f(x) in (7.1) has its largest value for x = n/2] and that for odd n, there
are two equal “largest" values of f(x), namely for x = (n + 1) and x = (n – 1).
Hint: Simplify the fraction f (x + 1)/ƒ(x), and then find the values of x for which
it is greater than 1 [that is, f(x + 1) > f(x)], and less than or equal to 1 [that is,
f (x + 1) < f(x)]. Remember that x must be an integer.
10.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ab45c84-c914-48f3-a579-425972c05b19%2F64161aad-8a29-41c3-b487-cc97e6963035%2Fpdmgtx_processed.png&w=3840&q=75)
Transcribed Image Text:Show that the most probable number of heads in n tosses of a coin is ;n for even n
[that is, f(x) in (7.1) has its largest value for x = n/2] and that for odd n, there
are two equal “largest" values of f(x), namely for x = (n + 1) and x = (n – 1).
Hint: Simplify the fraction f (x + 1)/ƒ(x), and then find the values of x for which
it is greater than 1 [that is, f(x + 1) > f(x)], and less than or equal to 1 [that is,
f (x + 1) < f(x)]. Remember that x must be an integer.
10.
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A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON