Weekly Experiment and Discussion - Part 2 - Due by Day 5 A) Given the results of your own experiment, can you conclude the results of each coin were independent? ( Show your supporting work) 1st coin Heads 1st coin Tails 2nd coin Heads 12 (H, H) 14 (T, H) 2nd coin tails 13of (H, T) 11 of (T, T) B) Using the compiled results can you conclude the results of each coin were independent? ( Show your supporting work) Note: For each, it is about interpreting the results versus any preconceived notions you may have about this exercise 1st coin Heads 1st coin Tails 2nd coin Heads 132 135 2nd coin tails 154 129 Clarification: ========== Two events A and B are independent if the conditional probability of one event using the other event as a condition is the same as the probability of the first event, that is P ( A | B) = P(A) and P(B | A) = P(B) these two conditions can be summarized into the criteria for independence for two events: P ( A and B ) = P(A) P(B) For two random variables X and Y to be independent the events of type { X = x } and { Y = y } need to be independent for every possible values of random variables x and y. Consider the outcome of the first coin a random variable, it has two values, H or T, and the outcome of the second coin a random variable with outcomes H and T. To verify the independence for two coin tosses, all four pairs of events need to be verified for independence: {First = H} { Second = H } {First = H} { Second = T } {First = T} { Second = H } {First = T} { Second = T } Please, feel free choose one pair to verify for each