Final answer:
The correct statement is that a probability distribution shows the likelihood of different outcomes for a random variable. The chi-square and t-distributions are related and as the degrees of freedom increase, their shapes become more similar. The symbols μ and σ represent the mean and standard deviation, respectively.
Step-by-step explanation:
Among the given statements about probability distributions, the correct option is: 'A probability distribution shows the likelihood of occurrence of specific outcomes of a random variable.' This means that a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes for an experiment. It's a statistical concept that encompasses various distributions such as the normal distribution, the chi-square distribution, and the Student's t-distribution.
The chi-square distribution and the t-distribution are indeed related; they are both used in the context of inferential statistics, particularly hypothesis testing. The chi-square distribution tends to become more symmetrical as the degrees of freedom increase. On the aspects of shape, the normal distribution and the Student's t-distribution are similar especially as the degrees of freedom increase for the t-distribution, making it more like the standard normal distribution. Lastly, the symbols used in distributions are standardized where 'μ' represents the mean, and 'σ' (sigma) denotes the standard deviation.