L2 - EE7750 MACHINERECOGNITIONOFPATTERNS...

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EE7750 MACHINE RECOGNITION OF PATTERNS Lecture 2: Probability and Statistics
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Probability Theory Apples and Oranges We randomly choose a box; draw an object randomly; and then put it back. Red box Blue box Red Blue Apple Orange 2 6 3 1 X Y
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Probability Theory Red box Blue box Red Blue Apple Orange 2 6 3 1 X Y Marginal probability: P(X=Red) Conditional probability: P(Y=Apple | X=Red) Joint probability: P(X=Blue, Y=Orange) Examples
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Probability Theory Red box Blue box Red Blue Apple Orange 2 6 3 1 X Y Suppose we pick red box for 40% of the time, and blue box 60% of the time; then P(Red) := P(X=Red) = 0.4 P(Blue) := P(X=Blue) = 0.6 Prior probabilities
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Probability Theory Red box Blue box Red Blue Apple Orange 2 6 3 1 X Y What is the probability of picking an Apple? P(Y=Apple) = P(Y=Apple | X=Red)*P(X=Red) + P(Y=Apple | X=Blue)*P(X=Blue) () ( ,) X PY PXY = (,) (| )() ( |)() PY X PX PX Y PY = =
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Probability Theory Red box Blue box Red Blue Apple Orange 2 6 3 1 X Y If the object I picked is Apple, what is the probability that it came from the Red box?
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L2 - EE7750 MACHINERECOGNITIONOFPATTERNS...

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