Probability mass function is alwaysa)0b)greater than 0c)greater than e...
Probability mass function (PMF) is a function that maps every possible outcome of a discrete random variable to a probability. It is used to describe the distribution of the random variable.
PMF is always greater than or equal to 0 because probabilities cannot be negative. If a PMF is negative for any value of the random variable, it would imply a negative probability, which is not possible.
Explanation:
Probability is a measure of the likelihood of an event occurring. It ranges from 0 to 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain. A probability mass function maps every possible outcome of a discrete random variable to a probability.
A discrete random variable has a finite or countably infinite set of possible outcomes. For example, the possible outcomes of rolling a fair six-sided die are 1, 2, 3, 4, 5, and 6. The probability of getting any of these outcomes is 1/6, which is the probability mass function of the random variable.
The PMF must satisfy the following conditions:
- Probability mass function is always greater than or equal to 0.
- The sum of the probabilities of all possible outcomes must be equal to 1.
If the PMF is negative for any value of the random variable, it would imply a negative probability, which is not possible. Therefore, the PMF must always be greater than or equal to 0.
Conclusion:
Probability mass function is always greater than or equal to 0 because probabilities cannot be negative. It is used to describe the distribution of a discrete random variable. The sum of the probabilities of all possible outcomes must be equal to 1.
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