1)Let X be a continous random variable with a uniform distribution on the range (0,θ). Find the mean and variance of X, along with its distribution function F(x)=P(X<=x).

2)suppose X1...Xn are independent identically distributed random variables, each with distribution function Fx(x). Let M be the largest of the {Xi}. express the event 'M<=x' as an intersection of n independent events, each involving exactly one of the {Xi}. hence deduce that the distribution function of M is Fm(x)=[Fx(x)]^n

3)use results of 1) and 2) to write down expression for the distribution function of the largest among n independent U(0,θ) random variables. find the corresponding density function.

2. Originally Posted by kevek
1)Let X be a continous random variable with a uniform distribution on the range (0,θ). Find the mean and variance of X, along with its distribution function F(x)=P(X<=x).

[snip]

I might have time for the others later.

3. Originally Posted by kevek
1)Let X be a continous random variable with a uniform distribution on the range (0,θ). Find the mean and variance of X, along with its distribution function F(x)=P(X<=x).

2)suppose X1...Xn are independent identically distributed random variables, each with distribution function Fx(x). Let M be the largest of the {Xi}. express the event 'M<=x' as an intersection of n independent events, each involving exactly one of the {Xi}. hence deduce that the distribution function of M is Fm(x)=[Fx(x)]^n

3)use results of 1) and 2) to write down expression for the distribution function of the largest among n independent U(0,θ) random variables. find the corresponding density function.
The ideas you need for 2) are in this thread: http://www.mathhelpforum.com/math-he...ease-help.html

If you're still stuck, please show where.

Where are you stuck in 3)?

4. Originally Posted by mr fantastic
The ideas you need for 2) are in this thread: http://www.mathhelpforum.com/math-he...ease-help.html

If you're still stuck, please show where.

Where are you stuck in 3)?
Thank you very much.
In part 3) i don't understand what is 'U( )' and what is corresponding density function

5. Originally Posted by kevek
Thank you very much.
In part 3) i don't understand what is 'U( )' and what is corresponding density function

For 2) this thread might also help: http://www.mathhelpforum.com/math-he...-question.html

U(0,θ) means the uniform distribution on the range (0,θ).