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Does t-distribution rely on degree of freedom?
Yes. The parameters of the t distribution are mean, variance and the degree of freedom. The degree of freedom is equal to n-1, where n is the sample size. As a rule of thumb, above a sample size of 100, the degrees of freedom will be insignificant and can be ignored, by using the normal distribution. Some textbooks state that above 30, the degrees of freedom can be ignored.
Does Chi-square distribution becomes more skewed as the degrees of freedom increase?
No- skewness parameter declines with increased degrees of freedom. skewness = sqrt(8/k) see link
What are the difference between static degrees of freedom and dynamic degrees of freedom?
Mass and damping are associated with the motion of a dynamic system. Degrees-of-freedom with mass or damping are often called dynamic degrees-of-freedom; degrees-of-freedom with stiffness are called static degrees-of-freedom. It is possible (and often desirable) in models of complex systems to have fewer dynamic degrees-of-freedom than static degrees-of-freedom.
How do you identify a normal curve?
You cannot. It has a characteristic bell-shaped curve but so does a Student's t with enough degrees of freedom. There are other distributions which, with suitable choice of parameters can be made to look very similar to the Normal curve.
What are characteristics of the X2?
It is not negative. it is positively skewed, and it approaches a normal distribution as the degrees of freedom increase. Its shape is NEVER based on the sample size.
