Would you please explain this? Try to simplify it as much as possible because it is a really hard topic.

Assume that we have an "unusual coin" that has the probability 0.3 for "head" and the probability 0.7 for "tail". Further, assume that we toss such a coin four times. Define a random variable X: number of "heads". It follows the the r.v. X has a binomial probability distribution; X~Bin(n, P) n = 4 P = 0.3. a) Show that X has a binomial probability distribution. (Give the reasons that imply this conclusion). b) Find (for x=0 x=1 x=2 x=3 och x=4) the probability function for the r.v. Use 4 decimal places. c) Draw the graph of the probability function. d) Find, using the definition, the expected value of the r.v. X. (Continued next page.) e) Find the expected value of the r.v. X using an adequate formula. Compare with the answer in d). f) Find, using the definition, the variance of the r.v. X. g) Find the variance of the r.v. X using an adequate formula. Compare with the answer in f). h) Find the distribution function for the random variable X. (Remember, a distribution function has to be defined for all values on the real line, i.e. x E R.) i) Draw the graph to the distribution function