- #1

lemonthree

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I am not sure about finding the limit of the integral when

it comes to finding the CDF using the distribution function technique.

I know that support of y is 0 ≤y<4, and it is

not a one-to-one transformation.

Now, I am confused with part b), finding the limits when calculating the cdf of Y.

Here's my working.

When -1<x<1, it's a two-to-one transformation, 0≤ y<1

P(Y≤y) = P(X^2≤y)

= P(

P(Y≤y) = P(X^2≤y)

= P(

The part I'm unsure is in bold. I just can't seem to determine what are the limits...

I've drawn the graph of f(x) against x and y against x, I know it's supposed to help me but I don't know how it relates.

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it comes to finding the CDF using the distribution function technique.

I know that support of y is 0 ≤y<4, and it is

not a one-to-one transformation.

Now, I am confused with part b), finding the limits when calculating the cdf of Y.

Here's my working.

When -1<x<1, it's a two-to-one transformation, 0≤ y<1

P(Y≤y) = P(X^2≤y)

= P(

**-sqrt(y)**≤ X ≤**sqrt(y)**)When -2<x<-1, it's a one-to-one transformation, 1< y<4P(Y≤y) = P(X^2≤y)

= P(

**-sqrt(y)**≤ X ≤**sqrt(y)**)The part I'm unsure is in bold. I just can't seem to determine what are the limits...

I've drawn the graph of f(x) against x and y against x, I know it's supposed to help me but I don't know how it relates.

[DESMOS]{"version":7,"graph":{"viewport":{"xmin":-10,"ymin":-12.5,"xmax":10,"ymax":12.5}},"randomSeed":"066490480d2a6d972d994e681ea97f80","expressions":{"list":[{"id":"2","type":"table","columns":[{"values":["-2","-1","0","1",""],"hidden":true,"id":"3","color":"#2d70b3","latex":"x"},{"values":["","","","",""],"id":"4","color":"#c74440","lines":true,"latex":"x^{2}"}]}]}}[/DESMOS]

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