The waiting time for the arrival of a bus at a stop is uniformly distributed in the interval [0, 12].  If we go to the bus stop, what is the probability that we will wait at least 9 minutes for a bus?

For the probability distribution of a discrete random variables, the probabilities of any single value of x is always

A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by   Please show complete solution.

Let X be the total number of groups of customers at Jellibabix's restaurant over one day in Lugdunum. Experience shows that X Poi(30). Each table (group of customers) orders at least one bottle of wine with probability p = 0.80. Suppose each table decides independently from other tables whether or not to order wine. If Y is the number of tables that ordered at least one bottle of wine, find the distribution of Y (hint: consider the distribution of Y given X = x).