Question

Let X_{1},X_{2},...,X_{6} be an i.i.d. random sample where each X_{i} is a continuous random variable with probability density function f(x)=e^{-(x-0)}, x>0 Find the probability density function for X_{6}.

Random variables
ANSWERED
asked 2021-05-12
Let \(X_{1},X_{2},...,X_{6}\) be an i.i.d. random sample where each \(X_{i}\) is a continuous random variable with probability density function
\(f(x)=e^{-(x-0)}, x>0\)
Find the probability density function for \(X_{6}\).

Answers (1)

2021-05-13
Step 1
We know,
\(f(x)=e^{-(x-0)},x>0\)
And,
\(X_{1}X_{2},...,X_{6}\)
are IID random variables
Step 2
Therefore,
\(f(X_{6})=e^{-(x_{6}-0)},x_{6}>0\)
0
 
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