P(x) 6. 0.2 7 0.2 0.3 9 0.2 10 0.1 1. Calculate the mean or the expected value of X 2. Calculate the variance of the random variable , X 3. Calculate the standard deviation of the random variable , X

If x is a binomial random variable, use the binomial probability table to find the probabilities below. a. P(x < 7) for n = 15, p = 0.8 b. P(x ≥ 13) for n = 20, p = 0.3 c. P(x = 2) for n = 25, p = 0.5

The following data represent the number of games played in each series of an annual tournament from 1933 to 2005. Complete parts​ (a) through​ (d) below.

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Find the probability that a family took at least 3 vacations last year. x 0 1 2 PO) 0.12 0.62 0.14 0.88 0.12 0.1 0.26 3 4 0.02 0.1

Show that the Geometric probability distribution, with parameter p, is a valid discrete probability distribution.

Assuming that workers' salaries in your company are uniformly distributed between $40,000 and $60,000 per year, find the probability that a randomly chosen worker earns an annual salary between $45,000 and $55,000.