By Tormod Naes
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Submit 12 months word: First released April twenty eighth 1989
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Additional resources for A user-friendly guide to multivariate calibration and classification
3 Can you guess a rule that distinguishes a situation which requires adding probabilities from one which requires multiplying them? Random Variables and Their Random Experiments Rolling dice, tossing coins, drawing cards from a deck are all examples of random experiments. It's not easy to give a precise definition of the term "random experiment" because the word "random" leads into a deep (and fascinating) philosophical quagmire. But we can easily get along without a precise definition. It's enough to have a heuristic definition which will not lead us astray.
1 Probability Distributions of Random Variables Probability Models There are situations so complex-you might even think chaotic-that any analysis would seem impossible. But often such situations yield to the techniques of statistics. With proper data and with proper analysis of that data, you may be able to say a lot. As this course proceeds, it will be interesting for you to see exactly how statistics is able to deal with these seemingly impossible situations. But it won't be at all what you expect.
Wouldn't you have immediately concluded that it comes up tails two-thirds of the time? You should have. Analytically, P(heads) + P(tails) = 1, 1/3 + P(tails) = 1, and so P(tails)= 1 - 1/3 = 2/3. Now please ... " (b) What in the definition of the term "random experiment" captures the idea of randomness? 5 Let X be the random variable which counts the number of dots on the uppermost face for one roll of a die: (a) Give the probability distribution for X assuming the die yields two dots on the uppermost face 50% of the time on average, with all other faces equally likely.
A user-friendly guide to multivariate calibration and classification by Tormod Naes