Probability and Inferences in Statistics - Term Paper Example

Download file to see previous pages The t-statistics are used for inferential purposes involving small samples or where the population variance is unknown. Finally, the chi-square statistics are used for inferential statistics related to correlations and associations. These are only some of the distributions but they indicate nevertheless the value of probability distribution for inferences in statistics.
In making inferences on the population based on sample characteristics, a man used probability distribution or probability density functions. Probability distributions or density functions associates a numeral to a probability value. Probability density functions are curves represented by mathematical equations that best capture the characteristics of the curve. In turn, the curves or the areas under the curve are associated with a probability level or probabilities.
Some of the probability density functions that are used in statistics are the binomial, hypergeometric, Poisson, normal and the chi-square distributions. In using any of the probability density function, a statistician assumes that the distribution represented by the probability density function best captures how the population or the data of the population is distributed. Alternatively, at least, the statistician assumes or believes that the distribution represented by the probability density function is most useful for him or her to infer population characteristics based on sample characteristics.
Among several probability density functions used in statistics, some of the more widely used are the normal distribution, the chi-square distribution, the F-distribution, and the binomial distribution. In this work, we focus on three probability density functions: two types of a normal probability density function and the chi-square distribution. The types of normal distribution are the standard normal and the t-distribution. ...Download file to see next pagesRead More