Task 1: Basic Probabilities and Visualizations (1)

Please provide the requested visualization as well as the numeric results. In both cases, please provide how you realized these (calculations, code, steps…) and why it is the appropriate tools. Do not forget to include the scale of each graphics so a reader can read the numbers represented.

• If ξ1 is 0: A vote with outcome for or against follows a Bernoulli distribution where P(vote="for")=ξ2. Represent the proportion of “for” and “against” in this single Bernoulli trial using a graphic and a percentage. Can an expectation be calculated? Justify your answer by all necessary hypotheses.

• If ξ1 is between 1 and 3: The number of meteorites falling on an ocean in a given year can be modelled by one of the following distributions. Give a graphic showing the probability of one, two, three… meteorites falling (until the probability remains provably less than 0.5% for any bigger number of meteorites). Calculate the expectation and median and show them graphically on this graphic:

o If ξ1 is 1: a Poisson distribution with an expectation of λ=ξ2

o If ξ1 is 2: a negative binomial distribution with number of successes of k=ξ2 und ????=ξ3.

o If ξ1 is 3: a geometric distribution counting the number of Bernoulli trials with p=ξ2 until it succeeds.