Lets say I have 10 random numbers U(0,1). I have a variable called B that is defined as B=max{U1,U2,...U10}

I want help to prove that the density function of B is given by;

f_B(r) = 10*r^9 where r is in the interval [0,1]

How can I show this?

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- Mar 18th 2011, 04:46 AMstordase39Deriving denisty function for a given random variable
Lets say I have 10 random numbers U(0,1). I have a variable called B that is defined as B=max{U1,U2,...U10}

I want help to prove that the density function of B is given by;

f_B(r) = 10*r^9 where r is in the interval [0,1]

How can I show this? - Mar 18th 2011, 04:57 AMgustavodecastro
You want to derive the density function of a maximum, where U1, ..., U10 follows an uniform distribution.

and the density function can be obtained by calculating its derivative. - Mar 19th 2011, 12:04 AMmatheagle
the idea is right, but the U's are part of B, not the argument.

using independence...

Since the cummulative distribution of a U(0,1) is when 0<r<1.

NOW differentiate wrt r, which is a Beta by the way. - Mar 19th 2011, 03:34 AMmr fantastic
- Mar 19th 2011, 05:11 PMgustavodecastro
Thank you, matheagle.