((using R program do the following ))

7. Purines in microRNAs. Suppose that for certain microRNA of size 20 the probability of a purine is binomially distributed with probability 0.7.

(a) What is the probability of 14 purines?

(b) What is the probability of less than or equal to 14 purines?

(c) What is the probability of strictly more than 10 purines? (

d) What is the probability that there are between 10 and 15 purines, inclusive?

(e) How many purines do you expect? In other words: What is the mean of the distribution?

(f) What is the standard deviation of the distribution?