# 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

Middle

Poisson Distribution The discrete probability distribution with probability function given by P(X=r) = (e-λλr)/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

Conclusion

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.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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