B if x has a standard normal distribution use part a to, Basic Statistics

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B if x has a standard normal distribution use part a to

The event {X₂ ≤ y} is equivalent to what event involving X itself?

b. If X has a standard normal distribution, use part (a) to write the integral that equals P(X₂ ≤ y). Then differentiate this with respect to y to obtain the pdf of X₂ [the square of a N(0, 1) variable]. Finally, show that X₂ has a chi-squared distribution with n = 1 df [see (4.10)]

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Basic Statistics: B if x has a standard normal distribution use part a to

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