Solve the below:
Q1. A city law-enforcement official has stated that 20% of the items sold by pawn shops within the city have been stolen. Ralph has just purchased 4 items from on of the city's pawn shops. Assuming that the official is correct, and for x = the number of Ralph's purchases that have been stolen, determine the following:
a. P(x = 0)
b. P(2 ≤ x)
c. P(1 ≤ x ≤ 3)
d. P(x ≤ 2)
Q2. Determine the mean, variance, and standard deviation of the following discrete probability distribution:
X 0 1 2
P(x) 0.60 0.30 0.10