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Statistics S2 - Terms to learn

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Introduction

© S.Campbell 22/01/03

STATISTICS S2

TERMS TO LEARN

Polynomial        Let x1,x2,….xn be real numbers,

Then anxn + an-1xn +…a1x +a0  is a polynomial (with real coefficients).  Can be defined as f(x).

Integration        The process of finding an integral of x.

f(x) dx

Definite integral can be found if there is values α and β

Factorial        For a positive integer the notation n! (n factorial) is used for n(n-1)(n-2)…x 2 x 1.  0!=1  4!=4 x 3 x 2 x 1

Binomial Coefficient        The number (nCr) = n!/r!(n-r)!

Binomial Distribution        The discrete probability distribution for the number of successes when n independent experiments are carried out, each with the same probability p of success.  

X~B(n,p)  P(X=r) = (nCr) x pr x (1-p)n - r

Independent Events        

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Middle

Poisson Distribution        The discrete probability distribution with probability function given by P(X=r) = (eλr)/r!  for r=0,1,2,…n where λ is a positive parameter.  λ=mean and varience.   X~Po(λ)

Continuous Random Variable        A quality that takes different numerical values according to the particular experiment.  It is continuous if the set of values forms an interval, finite or infinite.

Probability Density Function        For continuous random variable x, the p.d.f is:

P(a ≤ x ≥ b) =  ∫f(x)dx

Cumulative Distribution Function        For random variable x, the c.d.f is:

                                                F(x) = P(X ≤ x)

                                                F(x)  = ∑p(xi)

Mode        Most frequently occurring observation in a sample or, for grouped data, the group with the highest frequency.  

Median        Middle observation.  ½(n+1)

                For p.d.f ∫ f(x) dx = 0.5

Sample

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Conclusion

acceptance region and the critical (or rejection) region.  These depend upon the choice of significance level α , which is the probability that the test statistic lies in the critical region if H0 is true.  Often α is chosen to be 5% e.g. if the test statistic falls in the critical region, the null hypothesis H0 is rejected; otherwise the conclusion is that there is no evidence for rejecting H0 and it is said that H0is accepted.

The null hypothesis H0 normally specifies that a certain parameter has a certain value.  If the alternative hypothesis H1 says that the parameter is not equal to this value, then the test is said to be two-tailed.  If H1 says that the parameter is greater than this value (or less than) the test is one-tailed.

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