The probability equation for a survey and the number of speeding tickets, giving it a certain day any local neighborhood is given as Px =7-2x/20 where X can be zero, one, two, or three. Does this determine a probability distribution
Yes, the equation Px = (7-2x)/20 determines a probability distribution. To determine if it is indeed a probability distribution, we need to check if the probabilities given by the equation meet the requirements of a probability distribution.
1. The probabilities must be non-negative: Since the equation involves division by a positive number (20), the probabilities will always be non-negative for x = 0, 1, 2, or 3.
2. The sum of all probabilities must equal 1: We need to add up the probabilities for x = 0, 1, 2, and 3 and check if the sum equals 1.
P0 = (7-2(0))/20 = 7/20
P1 = (7-2(1))/20 = 5/20
P2 = (7-2(2))/20 = 3/20
P3 = (7-2(3))/20 = 1/20
Sum of probabilities = (7/20) + (5/20) + (3/20) + (1/20) = 16/20 = 4/5 = 0.8
Since the sum of all probabilities equals 1, we can conclude that the given equation determines a probability distribution.