Illustrate for each of the following conditions the random variable, provide the possible values of the random variable, state how the random variable is distributed (including the values for the parameters), compute the expectation value of the random variable and give the corresponding probability as an R-command.
a) 40 BE-students and 60 QUSH-students are writing a statistics exam in one lecture hall. They all hand in the exams randomly on just one pile. The professor picks the first ten exams. What is the probability that 7 of these exams are BE exams?
b) The exam takes one hour and each of the 100 students hands in his results at random points in time. What is the probability that the first students hands in his exam after less than 5 minutes?
c) What is the probability that the seventh student hands in his exam in an interval between 10 and 15 minutes?
d) The probability that a student feels confident after he has written the statistics exam is 0.3. What is the probability that more than 50 of the 100 students feel confident after they have written the exam?