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,

\(f(X_{6})=e^{-(x_{6}-0)},x_{6}>0\)

We know,

\(f(x)=e^{-(x-0)},x>0\)

And,

\(X_{1}X_{2},...,X_{6}\)

are IID random variables

Step 2

Therefore,

\(f(X_{6})=e^{-(x_{6}-0)},x_{6}>0\)