Prove that the quantity S= -kΣP li(P) r=1 is a maximum when P, = 1/n for all r. Do this by showing that S - kIn n < 0. [Hint: The inequality In[1/(nP,)] < 1/(nP,) – 1 will be helpful. To arrive at an expression in which you can use this inequality, you will have to insert E- P, = 1 in an appropriate place. This is a problem which is easier not using calculus because of the probability constraint.]
Prove that the quantity S= -kΣP li(P) r=1 is a maximum when P, = 1/n for all r. Do this by showing that S - kIn n < 0. [Hint: The inequality In[1/(nP,)] < 1/(nP,) – 1 will be helpful. To arrive at an expression in which you can use this inequality, you will have to insert E- P, = 1 in an appropriate place. This is a problem which is easier not using calculus because of the probability constraint.]
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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![Prove that the quantity
S= -kΣP li(P)
r=1
is a maximum when P, = 1/n for all r. Do this by showing that S - kIn n < 0. [Hint: The
inequality In[1/(nP,)] < 1/(nP,) – 1 will be helpful. To arrive at an expression in which you
can use this inequality, you will have to insert E- P, = 1 in an appropriate place. This is
a problem which is easier not using calculus because of the probability constraint.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F424c3c55-9c99-4f24-bee3-85bf667e2f9d%2Ff2c0c25a-e7a1-4f92-aa2e-1a70903e2c6f%2Ffb3m8z4_processed.png&w=3840&q=75)
Transcribed Image Text:Prove that the quantity
S= -kΣP li(P)
r=1
is a maximum when P, = 1/n for all r. Do this by showing that S - kIn n < 0. [Hint: The
inequality In[1/(nP,)] < 1/(nP,) – 1 will be helpful. To arrive at an expression in which you
can use this inequality, you will have to insert E- P, = 1 in an appropriate place. This is
a problem which is easier not using calculus because of the probability constraint.]
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