Probability and statistics

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Probability

Probability deals with predicting the likelihood of future events and it is primarily a theoretical branch of mathematics, which studies the consequences of mathematical definitions

Books

• http://www.quora.com/What-are-some-good-books-for-learning-probability-and-statistics
• Gonick, L. and Smith, W. (1993). The Cartoon Guide to Statistics. [online] Goodreads. Available at: https://www.goodreads.com/book/show/168872.The_Cartoon_Guide_to_Statistics?from_search=true [Accessed 4 Jul. 2014].

  References

• Wikipedia, (2014). List of probability distributions. [online] Available at: http://en.wikipedia.org/wiki/List_of_probability_distributions [Accessed 4 Jul. 2014].
• Cs.sunysb.edu, (2014). Probability versus Statistics. [online] Available at: http://www.cs.sunysb.edu/~skiena/jaialai/excerpts/node12.html [Accessed 4 Jul. 2014].

[rain1024]

Statistic

Statistics involves the analysis of the frequency of past events and it is primarily an applied branch of mathematics, which tries to make sense of observations in the real world.

Correlation

Statistical correlation is a statistical technique which tells us if two variables are related.

Correlation Coefficient

The coefficient of determination, r^2, is useful because it gives the proportion of the variance (fluctuation) of one variable that is predictable from the other variable. It is a measure that allows us to determine how certain one can be in making predictions from a certain model/graph. The coefficient of determination is the ratio of the explained variation to the total variation. The coefficient of determination is such that 0 < r 2 < 1, and denotes the strength of the linear association between x and y.
The coefficient of determination represents the percent of the data that is the closest to the line of best fit. For example, if r = 0.922, then r 2 = 0.850, which means that 85% of the total variation in y can be explained by the linear relationship between x and y (as described by the regression equation). The other 15% of the total variation in y remains unexplained. The coefficient of determination is a measure of how well the regression line represents the data. If the regression line passes exactly through every point on the scatter plot, it would be able to explain all of the variation. The further the line is away from the points, the less it is able to explain.

Coefficient of Determination

References

• Explorable.com, (2014). Statistical Correlation - Strength of Relationship Between Variables. [online] Available at: https://explorable.com/statistical-correlation [Accessed 4 Jul. 2014].
• Roberts, D. (2014). Statistics 2 - Correlation Coefficient and Coefficient of Determination. [online] Mathbits.com. Available at: http://mathbits.com/MathBits/TISection/Statistics2/correlation.htm [Accessed 4 Jul. 2014].
• Mathworld.wolfram.com, (2014). Correlation Coefficient -- from Wolfram MathWorld. [online] Available at: http://mathworld.wolfram.com/CorrelationCoefficient.html [Accessed 4 Jul. 2014].

[rain1024]

Distribution

Discrete distributions

Binomial distribution

Real world examples

Toss a fair coin three times ... what is the chance of getting two Heads?

Poisson distribution

Real world examples

The arrival of a weird particle from outer space at a counter on some farm outside Topeka, occurs on average 2 times per hour. But there are variations from that average. What is the probability that in a given hour three weird particles will be recorded?

Continuous distributions

Normal distribution

Laplace distribution

References

• Stat.ethz.ch, (2014). R: Distributions in the stats package. [online] Available at: http://stat.ethz.ch/R-manual/R-patched/library/stats/html/Distributions.html [Accessed 5 Jul. 2014].
• Umass.edu, (2014). Statistics | The Poisson Distribution. [online] Available at: http://www.umass.edu/wsp/resources/poisson/ [Accessed 5 Jul. 2014].