# iid random variables [duplicate]

Let X,Y,Z be independent, identically distributed random variables,each with density $$f(x)=6x^5$$ for $$0\leq x\leq1$$ and 0 elsewhere.I want to find the distribution and density functions of the maximum of X,Y and Z.

Answer:-I know by integrating density function, distribution function can be obtained.I computed CDF of maximum of $$X,Y,Z=X^6$$ and its PDF=$$18*X^{17}$$.

CDF of minimum of $$X,Y,Z=1-(1-X^6)^3$$ and its PDF is $$6*X^5*3*(1-X^6)^2$$

## marked as duplicate by whuber♦Feb 26 '16 at 15:58

• I have calculated distribution function of the max(X,Y,Z) which is $3x^{12}$. Whereas density function of the maximum of iid random variables X,Y,Z is $18x^{17}$.I want to give detailed answer, but I didn't find 'ANSWER' tab below this question. – Dhamnekar Winod May 28 '16 at 14:14
• Your calculation cannot be correct, because the integral of $3x^{12}$ over the interval $[0,1]$ is only $3/13$ rather than $1$. – whuber May 28 '16 at 18:17
• @whuber You are correct.You are rightly pointed out my mistake. Howsoever, after rectifying my mistake, the distribution function of max iid random variables is 3 and its density function is $18x^5$. I hope these would be correct answers. – Dhamnekar Winod May 29 '16 at 14:43
• Those values obviously are incorrect, for the same reason given before (and because no distribution function can equal $3$, since probabilities lie between $0$ and $1$). You should study the related threads more closely. – whuber May 29 '16 at 14:58