1. The following table displays a frequency distribution for the number of siblings for students at one middle school. For a randomly selected student in the school, let X denote the number of siblings of the student. Obtain the probability distribution of X. Number of siblings 0 1 2 3 4 5 6 7 Frequency 180 259 139 57 24 10 53 2. The number of loaves of rye bread left on the shelf of a local bakery at closing (denoted by the random variable X) varies from day to day. Past records show that the probability distribution of X is as shown in the following table. Find the probability that there will be at least three loaves left over at the end of any given day. 2 5 6 3 4 0.20 0.15 0.10 0.08 0.02 3. Suppose that D is a random variable. Given that P(D> 4.1) = 0.8, find P(D 4.1). 4. The random variable X is the number that shows up when a loaded die is rolled. Its probability distribution is given in the table. Find the mean and standard deviation of the random variable. X 1 0 P(X=x) 0.20 0.25 x|P(X=x) 0.14 0.11 0.15 0.10 0.14 0.36 1 2 3 4 5 6