An editor reading through my manuscript discovers that I make a lot of typograph
ID: 3130048 • Letter: A
Question
An editor reading through my manuscript discovers that I make a lot of typographical errors. In fact, I make a mistake at the rate of 7 per page (independent across pages). What is the expected number of mistakes I make on a randomly selected page? What is the expected number of mistakes I make on 10 pages? If we define X as the number of mistakes I make on a page, which distribution best describes X? What is the probability that I make no mistakes on a randomly selected page? What is the probability that I make 10 mistakes on a randomly selected page? On a random page, what is the minimum and maximum number of mistakes I can make? What is the expected number of mistakes I will make on a page and what is the variance?Explanation / Answer
1.
As given, we expect
E(x) = 7 [ANSWER, 7 MISTAKES PER PAGE]
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2.
Hence, for 10 pages,
E(10x) = 10E(x) = 10*7 = 70 [ANSWER]
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3.
It is a Poisson distribution with mean 7. [ANSWER]
We chose Poisson distirbution as the mean number of successes per page is constant.
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4.
Note that the probability of x successes is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 7
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.000911882 [ANSWER]
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5.
Note that the probability of x successes is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 7
x = the number of successes = 10
Thus, the probability is
P ( 10 ) = 0.070983269 [ANSWER]
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6.
You can make a minimum of 0 mistakes, but there is not upper limit for number of mistakes.
Minimum: 0
Maximum: infinity
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7.
As we said,
E(x) = 7 [EXPECTED NUMBER OF MISTAKES]
As for Poisson distirbution,
Variance = E(x)
Then
Variance = 7 [ANSWER, VARIANCE]
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