Select a balanced coin and toss it 100 times. Record the outcomes you get by assigning 10 to a head and 0 to a tail. Suppose the random variable X represents the number of heads in tossing.

A) Calculate the mean of X based on your experiment. Show the distribution of your experiment in the PDF file, use two decimals for your answer.

B)Let's now assume that you toss this coin an infinite number of times (this is a theoretical assumption, you do not need to throw the coin). Assign 10 to a head and assign 0 to a tail.Suppose the random variable X represents the number of heads in the long run.

Estimate the mean of X based on this scenario. Show your reasoning in the PDF file.

C)From the experiment when you flip the coin 100 times, select 6 flips of the coin at random and calculate the average of those attempts (10 heads, 0 tails). Report the value of X_bar, show your work in the PDF file.

D)Now, let's assume that you can create an infinite number of samples of n=6 and calculate their mean of X assigning 10 to heads and 0 to tails. Calculate the E(X_bar), show your work in the PDF file

E)Now, compare and contrast your answers for:

• Mean(X) for 100 attempts,
• Mean(X) for an infinite number of attempts,
• (X_bar) for one sample of size n=6 with randomly selected attempts, and
• E(X_bar) if we were to repeat an infinite number of samples of size n=6.

Explain your findings.