- #1

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Going by how the book taught it I would start this problem by computing the inverse of g(x). However this function has no inverse. Any suggestions how to proceed?

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- Thread starter dizzle1518
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- #1

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Going by how the book taught it I would start this problem by computing the inverse of g(x). However this function has no inverse. Any suggestions how to proceed?

- #2

Stephen Tashi

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- #4

Stephen Tashi

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Are you taking about the interval to use when computing the cumulative distribution of Y? Yes, that's right if you're using [tex]\Phi [/tex] to denote the cumulative normal.

The wording of the problem indicates that you should specify a finite list of integers on which the density of Y is non-zero.

- #5

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I e-mailed my teacher and she replied with the below:

"No, for every y the corresponding interval for x has to be (-infinity,[y]). The endpoint should be an integer."

Does she mean it should be Fy=phi(y)??

- #6

Stephen Tashi

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How would you know which integers to specify anyway?

There can't be that many integers with a significant probability. The standard normal has standard deviation = 1. There isn't much chance of getting Y = 12.

You didn't say what you asked your teacher, so I don't what her answer meant.

- #7

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There can't be that many integers with a significant probability. The standard normal has standard deviation = 1. There isn't much chance of getting Y = 12.

got you. then picking up to what numbers you want to define the distribution of Y is up to the person solving the problem?

You didn't say what you asked your teacher, so I don't what her answer meant.

i asked her the same thing, i.e. if the interval was (-infinity, y-1) and if the distribution of Y is phi(y-1), and thats what she answered

- #8

Stephen Tashi

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got you. then picking up to what numbers you want to define the distribution of Y is up to the person solving the problem?

It's up to them to do the work. There won't be much disagreement on which integers have non-zero probability if they all use similar tables of the normal distribution.

i asked her the same thing, i.e. if the interval was (-infinity, y-1) and if the distribution of Y is phi(y-1), and thats what she answered

The phrase "if the interval was (-infinity, y-1)" isn't a complete sentence. So I assume she ignored it.

The answer to "if the distribution of Y is phi(y-1)" is no. She answered correctly. The distribution of Y isn't defined on all real numbers, only on integers. Her answer indicates that you only use the calculation on integer values of Y.

- #9

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so what would be the distribution of Y then?

- #10

Stephen Tashi

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You have the correct idea about using [tex] \phi [/tex]. It's the imprecision in your statement of that idea that your teacher objects to. However, I don't think stating the formula for the cumulative distribution of Y is what the problem requests.

- #11

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Are you in doubt about how to compute the numerical probability that Y = 1 or Y = -1 ?

a bit yes

I think the problem wants you give the probability density for Y, not the cumulative distribution.

would Y have a density or mass function? i thought mass since Y is defined over integers only. the fact that X is continuous and Y discrete is throwing me off somewhat.

- #12

Stephen Tashi

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