6. Let X be a random variable that denotes the number of tails in a set of 30 tosses.

a) What is the sample space for ?

b) Assume that the coin is unfair with () = 0.55. Assuming independent toss outcomes, what

probability distribution can you use to model ? Make sure to name the distribution and the values

of any parameters.

c) What are () = and based on the distribution named in part (b) above? Interpret these

numbers.

d) What is the exact probability that > 6 in any given case? Write down the formula you would use

with numbers substituted but use R to calculate the answer. Copy and paste your R code here with

the answer from R.

e) Explain why the number of heads out in a set of 30 tosses can be modeled as a binomial random

variable, , with parameters = 30 and = 0.45.