- #1

EngWiPy

- 1,368

- 61

Suppose X is a Chi-square random variable. Then what is:

[tex]\text{Pr}\left\{X<b\right\}[/tex]?

Does the above probability is the CDF of X? The only difference is that there is no equality!

Thanks

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- Thread starter EngWiPy
- Start date

- #1

EngWiPy

- 1,368

- 61

Suppose X is a Chi-square random variable. Then what is:

[tex]\text{Pr}\left\{X<b\right\}[/tex]?

Does the above probability is the CDF of X? The only difference is that there is no equality!

Thanks

- #2

Bacle2

Science Advisor

- 1,089

- 10

Have you checked the definitions, e.g:

http://en.wikipedia.org/wiki/Chi-squared_distribution

- #3

EngWiPy

- 1,368

- 61

My question can we say that Pr[X<b] approximately equal Pr[X<=b]?

- #4

awkward

- 365

- 0

P(X < b) = P(X <= b) for continuous distributions, for example the chi-square distribution.

- #5

- 15,450

- 688

Not approximately equal. Exactly equal.My question can we say that Pr[X<b] approximately equal Pr[X<=b]?

The only time this isn't the case is with those non-continuous random variables for which P(x=b) can be non-zero for some values of b. This doesn't apply to the chi square distribution, which is an absolutely continuous probability distribution. "Absolutely continuous" essentially means it has a PDF; this a stronger constraint than merely being continuous.

- #6

EngWiPy

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- 61

Thanks all

- #7

Bacle2

Science Advisor

- 1,089

- 10

singletons is that an uncountable sum cannot converge unless only countably-many

terms are non-zero.

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