So I have to prove that n*Ymin is an unbiased estimator for lambda from the distribution:

(1/lambda)e^(-x/lambda)

I kno to show that the estimator is unbiased requires that its expected value to equal the given parameter.

For Ymin I got: {n(1+e^(-x/lambda))}*((1/lambda)e^(-x/lambda)

I know that for taking the expected value of this is multiplying by x and then integrating but this seems WAY too complicated based on what we have done so far.

Any help would be great!!!