Question
Explain the Uniform, Normal, Chi-square, t and F distributions. Highlight the relationships among these
distributions
Answer :
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Probability distributions are mathematical models used to describe the behaviour of random variables. In Mathematical Foundations-II, the Uniform, Normal, Chi-square, t and F distributions are important continuous probability distributions. They are widely used in statistical inference, estimation, hypothesis testing and analysis of variance. The Uniform distribution is one of the simplest continuous distributions. If a random variable (X) is uniformly distributed over the interval ([a,b]), every value within this interval has equal probability density. Its probability density function is [ f(x)=\frac{1}{b-a}, \quad a\leq x\leq b. ] The mean is ((a+b)/2), while the variance is ((b-a)^2/12). The Uniform distribution is useful for modelling situations in which all outcomes within a specified range are equally likely. It is also important in simulation and random-number generation. The Normal distribution is a symmetric, bell-shaped continuous distribution. It is determined by its mean (\mu) and variance (\sigma^2),
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