Question

Which statement about the mean of a discrete random variable is not true or are they all true?

1) The mean is the sum of all possible values of the random variable multiplied by their respective probabilities.
2) The mean is a measure of central tendency.
3) The mean is always an integer.
4) The mean can be calculated using the formula E(X) = Σ(x * P(X = x))
5) Cannot be determined

Answer 1

The statement that the mean of a discrete random variable is always an integer is not true. The mean is the expected value and can represent any real number based on the outcomes and probabilities.

Step-by-step explanation:

The mean of a discrete random variable is not always an integer. This is the statement that is not true among the options provided. The mean or expected value of a discrete random variable, represented by E(X) or μ, is calculated as the sum of all possible values of the random variable multiplied by their respective probabilities, which is a measure of central tendency. This is accurately computed using the formula E(X) = Σ(x * P(X = x)). While the mean is the long-term average of many trials of a statistical experiment, it does not need to be an integer as it can represent any real number depending on the outcomes and their probabilities.