• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Statistics S2 - Terms to learn

Extracts from this document...

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        

...read more.

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

...read more.

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.

...read more.

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

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Probability & Statistics essays

  1. Study of the height/diameter ratio of limpets inhabiting the middle shore region of exposed ...

    Identify the limpets that are closest to the four corners of the quadrat and the one closest to the middle (see picture 3). Use the vernier callipers to measure their height and diameter.* Remember to be accurate to 0.05 millimetres (Be careful with the metal rod sticking out of the calliper!)

  2. Descriptive Statistics 1. Mean, median and mode.

    and a standard deviation of 15 (standard deviation is a measure of spread from the mean and we will discuss it in greater detail later in the course). I then took 40 samples of 5 numbers and 40 samples of 20 numbers from the population.

  1. Teenagers and Computers Data And Statistics Project

    x 12 = 96 The 3 face corners will always be 8 6. Formula Explanation The first formula that I worked out was the total no of cubes, this was simple as to measure the volume of a cube is to cube the length that you have.

  2. Driving test

    In the data, some of the driver's are missing their "number of mistakes". I will use my formula to fill in some of this missing data: Driver Gender Lessons Mistakes 63 M 32 -0.2x32+22.7 =16 74 F 24 -0.2x24+22.7 =17 118 F 39 -0.2x39+22.7 =14 216 M 18 -0.2x18+23.7 =19

  1. Estimating the length of a line and the size of an angle.

    So it is an unsuitable method to use. Also sometimes you might not get enough people in the year group you want to represent the population sample, which distorts the data. While the advantage of it is that it is easy to get the information needed and is very cheap

  2. Fantasy Football - Maths Coursework - Statistics

    You get 5 points for each goal and an extra 5 points if you score 3 or more goals. I think that attackers will also score more because unless they are booked during the game, there is no way for them to loose points, unlike defenders who loose points for conceding goals.

  1. GCSE Mathematics Coursework: Statistics Project

    1150 To find the number of Yr 7s of which should be girls in the sample: 124 x 24 = 11 (to nearest whole number) 275 Therefore, the number of male Yr 7s in the sample should be 13. To check: 151 x 24 = 13 (to nearest whole number)

  2. Identifying Relationships -Introduction to Statistical Inference.

    In some cases this is all that will be required. A graphical presentation can help with this. ( see Week 5 lecture for the SPSS commands to produce this type of graph ) The Research Question Investigate whether the acceptance of package customers is associated with the type of hotel?

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work