Question

Fill in the P (X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are 0, 1, 4, 5, and 6.

P ( X = x)
0: 0.30
1: 0.19
4:
5: 0.27
6:

Answer 1

A probability distribution for a discrete random variable X assigns probabilities to each possible value of X such that the sum of all probabilities is equal to 1. In this case, the possible values of X are 0, 1, 4, 5, and 6. You have provided the probabilities for X = 0, X = 1, and X = 5 as 0.30, 0.19, and 0.27 respectively.

The sum of these probabilities is 0.30 + 0.19 + 0.27 = 0.76. Since the sum of all probabilities must be equal to 1, the sum of the probabilities for X = 4 and X = 6 must be equal to 1 - 0.76 = 0.24.

Therefore, you can assign any non-negative values to P(X = 4) and P(X = 6) such that their sum is equal to 0.24 to give a legitimate probability distribution for the discrete random variable X.

For example, one possible probability distribution could be:

P(X = x) 0: 0.30 1: 0.19 4: 0.12 5: 0.27 6: 0.12