Who'll help me solve these tough questions? Ensure your answers are correct and provide clear illustrations and examples where necessary.

1. Having a pack of 52 cards, Jacob draws 5 cards. Determine the probability of having only 2 face from the ones drawn. Explain

2. From a population consisting of 16 items, a hypergeometric experiment is conducted where there are two successes out of the 4 total trials done. Determine the hypergeometric distribution expectations.

3. Determine in a Poisson distribution the mean value where n represents trials and p the success rate.

4. Determine the variance of a Poisson distribution where 'm' is the termed as the mean.

5. Determine the p.d.f. of a Poisson distribution.

6. Supposing that M represents the mean in a Poisson distribution, how can you determine the standard deviation?

7. Would it by any chance be misleading to state that the mean and variance in a Poisson distribution are equal?

8. Determine and evaluate the value of P(X) in a Poisson distribution given that the mean equals 'e'.

9. Solve for P(0) where you are given the mean distribution as m. Show illustration.

10. Illustrate and demonstrate how you determine in Poisson distribution the relationship of recurrence between P(x) and P(x +1).