Good afternoon,
I'm trying to solve the following problem:
I have a uniform random variable X with:
1 if 0 < x < 1
0 otherwise
Now, I computed the CDF in the following way:
0 if x <= 0
x if 0 < x < 1
1 if x equal or higher than 1
Then, the problem says, let Y = -2log X; it asks to find the quantile function.
The quantile function is the inverse of CDF. So I wrote:
F(y) =P(Y<= y) = P (-2log X <= y) = P (log x >= -y/2) = P ( x >= e ^ (-y/2) ) = 1 - P ( x <= e ^ (-y/2) ) = 1 - F( e^-(y/2) )
Then, I don't know what should I do next. The CDF is 1- e^ -(y/2) if y> 0 ?
If so, the CDF above seems to be the CDF of the exponential if lambda = 1/2. Is that the case? Can be that even though X is uniform r.v. ?
Thanks
I'm trying to solve the following problem:
I have a uniform random variable X with:
1 if 0 < x < 1
0 otherwise
Now, I computed the CDF in the following way:
0 if x <= 0
x if 0 < x < 1
1 if x equal or higher than 1
Then, the problem says, let Y = -2log X; it asks to find the quantile function.
The quantile function is the inverse of CDF. So I wrote:
F(y) =P(Y<= y) = P (-2log X <= y) = P (log x >= -y/2) = P ( x >= e ^ (-y/2) ) = 1 - P ( x <= e ^ (-y/2) ) = 1 - F( e^-(y/2) )
Then, I don't know what should I do next. The CDF is 1- e^ -(y/2) if y> 0 ?
If so, the CDF above seems to be the CDF of the exponential if lambda = 1/2. Is that the case? Can be that even though X is uniform r.v. ?
Thanks
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