Part A: Human beings aren’t good at being random Think about flipping a fair coin 100 times and recording

Part A: Human beings aren’t good at being random

Think about flipping a fair coin 100 times and recording H for heads and T for tails as you go along. You’d end up with 100 random Hs and Ts in a string. Because you have studied statistics you expect roughly 50Hs—maybe 47 or 51—but probably not 94 Hs and 6 Ts. Do your best to write out such a random string.
This is my string (I made up):
THHTHTHHTT
HTTTHTHHHT
THHTTHHHTT
THTHTTHTHH
THTHTTHTHH
TTHTTHTTHH
THHHTTTHTH
HHTTHTTHTH
HHTHTTHTTH
HTTHTHHTTH
Now really flip a coin 100 times, recording H and T in order.
Part B: Sampling and Random Variable
Mark 10 pennies (with numbers 1-10) and put in jar with 15 unmarked pennies. Shake jar. Without looking, pull out 3 and record how many of them are marked (with a number). You will get 0, 1, 2, or 3 marked coins.
How many different samples of 3 pennies out of 25 can you get? (Order does not matter). The answer is 2,300. Why? Show the answer.
How many of those samples would have 0, 1, 2, or 3 marked coins?

Show why 3 ^rd column count should be 675.
Counting the number of marked coins gives us a discrete random variable, X. Find:
P(X=0)
P(X=1)
P(X=2)
P(X=3)
Now, put the 10 marked coins in a jar with 15 unmarked coins. Shake, pull out 3 without looking. Write down the number of marked coins. Put them all back, shake, draw again and count marked coins again. Do this a total of 20 times. Now you have 20 pieces of data. Write down the data set. Compute the sample proportions. How do your sample proportions compare to the probabilities you computed above? Find the mean and standard deviation of the data set. Are the expected value and standard deviation of the random variable close to the mean and standard deviation of the data set? Should they be? Why? *Show all work. *Answer in complete sentences.