And giving probability equation is Px =2x-1/16 where X can be one, two, three, or four. Does this determine the probability distribution?
No, the given equation Px = (2x-1)/16 does not determine the probability distribution because it does not satisfy the requirements for a probability distribution. In order for a function to represent a probability distribution, it must meet two criteria:
1. The sum of all probabilities must equal 1: ∑Px = 1
2. Each individual probability must be between 0 and 1: 0 ≤ Px ≤ 1
We can check if the given equation satisfies these criteria by substituting the given values of x (1, 2, 3, 4) and calculating the probabilities:
P1 = (2(1)-1)/16 = 1/16
P2 = (2(2)-1)/16 = 3/16
P3 = (2(3)-1)/16 = 5/16
P4 = (2(4)-1)/16 = 7/16
Now, let's calculate the sum of all probabilities: P1 + P2 + P3 + P4 = (1/16) + (3/16) + (5/16) + (7/16) = 16/16 = 1
So, the given equation does satisfy the first criterion, i.e., the sum of all probabilities equals 1. However, some of the probabilities calculated are greater than 1 (e.g., P4 = 7/16). Therefore, the second criterion is not met, meaning this equation does not determine a valid probability distribution.