Simple Probability Problem

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Presentation transcript:

Simple Probability Problem Imagine I randomly choose 2 people from this class. What is the probability that both are in the same laboratory section?

Sample vs Population (true mean) (sample mean) (sample variance) (true variance) (sample mean) (sample variance)

Populations Parameters and Sample Statistics Population parameters include its true mean, variance and standard deviation (square root of the variance): Sample statistics with statistical inference can be used to estimate their corresponding population parameters to within an uncertainty.

Populations Parameters and Sample Statistics A sample is a finite-member representation of an ‘infinite’-member population. Sample statistics include its sample mean, variance and standard deviation (square root of the variance):

Normally Distributed Population using MATLAB’s command randtool

Random Sample of 50

Another Random Sample of 50

The Histogram Time record Histogram of digital data Figure 7.3 Figure 7.4 Time record Histogram of digital data analog, discrete, and digital signals 10 digital values: 1.5, 1.0, 2.5, 4.0, 3.5, 2.0, 2.5, 3.0, 2.5 and 0.5 V resorted in order: 0.5, 1.0, 1.5, 2.0, 2.5, 2.5, 2.5, 3.0, 3.5, 4.0 V N = 9 occurrences; j = 8 cells; nj = occurrences in j-th cell The histogram is a plot of nj (ordinate) versus magnitude (abscissa).

Proper Choice of Δx High K  small Δx The choice of Δx is critical to the interpretation of the histogram. Figure 7.5

Histogram Construction Rules To construct equal-width histograms: Identify the minimum and maximum values of x and its range where xrange = xmax – xmin. Determine K class intervals (usually use K = 1.15N1/3). Calculate Δx = xrange / K. Determine nj (j = 1 to K) in each Δx interval. Note ∑nj = N. Check that nj > 5 AND Δx ≥ Ux. Plot nj versus xmj,where xmj is the midpoint value of each interval.

Frequency Distribution The frequency distribution is a plot of nj /N versus magnitude. It is very similar to the histogram. Figure 7.7

Histograms and Frequency Distributions in LabVIEW ‘digital’ case ‘continuous’ case