For a discrete random variable, the mean will equal the most probable outcome of the probability distribution. True or false?
False.
The mean of a discrete random variable is calculated by multiplying each possible value by its corresponding probability and summing all these products. It represents the average value of the variable, not necessarily the most probable outcome. The most probable outcome is the value with the highest probability in the probability distribution.
False. For a discrete random variable, the mean is not necessarily equal to the most probable outcome of the probability distribution. The mean, also called the expected value, is a measure of the central tendency of the random variable and is calculated by multiplying each possible outcome by its probability and summing them up. It represents the long-term average value we would expect to observe over many repetitions of the experiment. On the other hand, the most probable outcome is simply the outcome with the highest probability. While the most probable outcome can provide some insight into the distribution, it does not necessarily represent the mean value.
False.
For a discrete random variable, the mean is calculated by summing the products of each possible outcome with its corresponding probability. It represents the average value or expected value of the variable. The most probable outcome is the mode, which is the value(s) that occur with the highest frequency in the probability distribution. In general, the mean and mode may or may not be equal for a discrete random variable.