A fair die is rolled, and then a coin with probability p of Heads is flipped as many times as the die roll says, e.g., if the result of the die roll is a 3, then the coin is flipped 3 times. Let X be the result of the die roll and Y be the number of times the coin lands Heads. (a) Find the joint PMF of X and Y . Are they independent? (b) Find the marginal PMFs of X and Y . (c) Find the conditional PMFs of Y given X = x and of Y given X = x.

BoxPlot is a way to show 5 number summary. The actual boxcovers the middle 50% of data (from Q1 to Q3) Multiple box plots are used to make comparisons. DotPlot are used to display 5 number summary as well. It is generally used for smaller data because a dot is used for each individual value. Where do outliars come from Human error, data entered wrong Improper values, ex....