look at the empirical distribution of 3000 prisoner’s heights.
Compute the corresponding discrete probability distribution
Compute the key statistics of this distribution (mean and variance)
Assume that the data are normally distributed with the same mean and variance as empirically calculated
Calculate the discrete probability distribution of the data as if they were normally distributed, but using the CUMULATIVE distribution function of the normal density! (note that in class we did not use the cumulative distribution)
Can you comment on the results?
Look at the binomial distribution of 100 flips of a coin
What is the probability of having exactly 50 heads?
can you explain why it is so low? Is it really counterintuitive or can you explain?
You flip the coin 100 times, but you are not sure if the coin is unbiased or biased. Your result is 40 Heads. Using the material provided in the XLS, do you think the coin is biased or legit? Why? [HINT: first, you must define a confidence level, say for example 90%, and then check on the XLS approximately which results are inside and outside that range. See also the notes on the XLS] Would your answer change if your boss asks you to be quite strict in your judgement? [HINT: stricter means a smaller “acceptance” region, or equivalently larger “rejection” region..] How would you do that? Please explain briefly
Consider the joint probability distribution in the XLS file for this week. Call X the variable on horizontal axis and Y the variable on the vertical axis.
Can you determine the joint probability of having X=15 and Y=19?
Can you determine the probability that X=15?
Can you determine the probability that Y=19.5?
Can you extract from the table (joint probability for two variables) the discrete probability function f(X) and F(Y) (probabilities for one variable only)? How?