Need help with 2 advanced stat questions

[NYCStats22]

Really need help with these two questions. I have been working on them for some time and just can't seem to make any significant progress


1) X is a continuous random variable with density function

f(x) = (θ + 1)x^θ , 0 < x < 1 and 0 elsewhere

Derive both the method of moments estimator and the maximum likelihood estimator for λ.

*For the MOM estimator you will need to find the mean*


2) Two surgical procedures are compares and what is of interest are the complication rates. 150 patients had procedure A and there were 35 complications while procedure B tested 138 patients and there were 34 complications. Does this indicate a difference at a 1% level. What is the P-value?

 

[mfb]

I have been working on them for some time

Please show your work then.
In addition, do you know the definitions of the things you have to calculate? Do you know formulas for them?

 

[statdad]

You don't have enough information to find the estimators for $\lambda$. Perhaps you should try for the
appropriate estimators of $\theta$.

Do you know how, in principle, to find a method of moments estimator? Same for the MLE. If so, set things up and work as far as possible, then organize your questions about what you have and what you need to do.