Using Rstudio, please show work

Suppose you are responsible for a clinical trial with 75 participants. Each participant in the trial has a condition, and the drug being tested is estimated to have a 45% success rate for curing the condition. Let X be the number of trial participants who are cleared of their condition by the drug.

a. What is the expected value and standard deviation of the number of cured patients in the trial. Hint: Assume that X is a binomially-distributed random variable. What are n and p?

b. Find the probability of all possible values of X both numerically and graphically.

c. As stated above, the assumed efficacy of the drug is 45%. The pharmaceutical company who makes the drug will scrap further R&D into the drug if they find evidence that the effectiveness is at or below 30%. What is the probability of such a finding in this clinical trial, assuming that the true effectiveness of the drug is indeed 45%?

d. Now let's assume that the pharmaceutical company has sufficient money to run as many trials as they please. In fact, let's simulate 10,000 trials as described above. You can do so using rbinom(10000, n, p). Estimate the mean and standard deviation of this using the built-in mean() and sd() functions in R.

Contrast these results to those from part a. How and why are they different?