Chapter 4 - Probability Topics.pdf

Chapter 4 - Probability Topics.pdf - Chapter 4 Probability...

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Chapter 4 – Probability Review Sheet (MA 511) 4.1 Density Histograms * Instead of using relative frequency for height in a histogram we use density instead when we want to reflect a percentage of time a class occurs. This has two advantages. 1) You can use classes of different widths. A height of relative frequency would be visually deceiving – but use of density relates area to probability of the class. This is ideal. 2) The total area of 1 maps to a probability space. 4.2 Probability Notions The Bernoulli Trial is a simple “Success/Failure” result. It has probability of success of p and failure of q = 1 – p. It’s a simple start but the backbone of the important Binomial Distribution we see later. Keep the concept of experiment (random phenomenon), outcome, and events clearly distinguished when doing a probability problem. The addition rule stated on p140 accounts for disjoint events. As long as events “A” and “B” do not share outcomes ( P(A and B) = 0 ) then you can use this concept. The addition rule of P(A or B) = P(A) + P(B) should be only used for disjoint events; otherwise P(A or B) = P(A) + P(B) – P(A and B) should be noted as the general addition rule. In statistics our distributions often just depend on the disjoint addition rule. P(E) = k/m is noted on p141; but this is a special case of equally likely outcomes. Random sampling fits this form– each sample should have equal chance of occurring. k = 1 but m = N C n; an astronomically huge number for typically sized populations and samples. We rarely ask what the probability of one random sample in practice is.
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