Question

Determine if the following could be a probability distribution for a discrete random variable, X. If no, state why.

X 20 30 40 50
P(X=x) 1.1 0.6 .2 .1

Answer 1

The given values cannot represent a probability distribution for a discrete random variable because there is a probability greater than 1 (1.1 for X=20), and the sum of all probabilities (2.0) does not equal 1.

Step-by-step explanation:

To determine if the given values could be a probability distribution for a discrete random variable X, we need to check two main conditions:

• The probability of each outcome (P(X=x)) must be between 0 and 1.
• The sum of all probabilities must equal 1.

In the given data, X = {20, 30, 40, 50} and the corresponding probabilities are {1.1, 0.6, 0.2, 0.1}. Immediately, we can see that the probability of 1.1 is not valid because it is greater than 1. Moreover, when you add all the given probabilities (1.1 + 0.6 + 0.2 + 0.1), the sum is 2.0, which is not equal to 1. Hence, the given values cannot represent a probability distribution function (PDF) for a discrete random variable.

The correct probability distribution must have probabilities that sum to 1.0 and each individual probability must be between 0 and 1, inclusive.