Please assist in this homework practical. Please also provide a written solution as well as screenshots of R outputs for a,b,c,d for extra practice.

The negative binomial is the distribution of the number of failures till the kth success, in independent Bernoulli trials. The probability of success at each trial is 7. This is denoted as Y ~ Negbin(k, 7) and has probability density function f(y) = (y+k- 1) k - 1 (1 - 7)37h, y= 0, 1, ..., & 0