Deriving 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?

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.

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.

Quote:

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Originally Posted by stordase39

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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Do some research/background reading on Order Statistics.

Thank you, matheagle.