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lemonthree
Member
 Apr 11, 2016
 51
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 onetoone 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 twotoone transformation, 0≤ y<1
P(Y≤y) = P(X^2≤y)
= P(sqrt(y) ≤ X ≤ sqrt(y) )
When 2<x<1, it's a onetoone transformation, 1< y<4
P(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.
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 onetoone 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 twotoone transformation, 0≤ y<1
P(Y≤y) = P(X^2≤y)
= P(sqrt(y) ≤ X ≤ sqrt(y) )
When 2<x<1, it's a onetoone transformation, 1< y<4
P(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.
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