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UNR, MATH/STAT 352, Spring 2007

Probability and Statistics. MATH/STAT 352. Spring 2007. Lecture 5: Probability, Bayes Theorem. (slides only contain intro). UNR, MATH/STAT 352, Spring 2007. Relevant problems. UNR, MATH/STAT 352, Spring 2007. Radar target detection. How reliable is the signal on the screen?

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UNR, MATH/STAT 352, Spring 2007

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  1. Probability and Statistics MATH/STAT 352 Spring 2007 Lecture 5: Probability, Bayes Theorem (slides only contain intro) UNR, MATH/STAT 352, Spring 2007

  2. Relevant problems UNR, MATH/STAT 352, Spring 2007

  3. Radar target detection How reliable is the signal on the screen? (Is it a target of a false alarm?) UNR, MATH/STAT 352, Spring 2007

  4. Medical screening How reliable is the positive test? (Is it a disease or a false alarm?) UNR, MATH/STAT 352, Spring 2007

  5. How does probability help to answer such questions? UNR, MATH/STAT 352, Spring 2007

  6. Deck of playing cards (52 cards) Four suits Thirteen cards in each suit hearts spades 2,3,4,5,6,7,8,9,10,J,Q,K,A Faces: Jack, Queen, King clubs diamonds UNR, MATH/STAT 352, Spring 2007

  7. Deck of playing cards Sample space for “taking one card at random from a deck” UNR, MATH/STAT 352, Spring 2007

  8. Is a randomly chosen card the Queen of Spades? P(Q♠) = 1/52 ≈ 0.02 UNR, MATH/STAT 352, Spring 2007

  9. Is a randomly chosen card a Queen? P(Q) = 4/52 =1/13 ≈ 0.08 UNR, MATH/STAT 352, Spring 2007

  10. Is a randomly chosen RED card a Queen? P(Q|red) = 2/26 =1/13 ≈ 0.08 UNR, MATH/STAT 352, Spring 2007

  11. Is a randomly chosen FACE card a Queen? P(Q|face) = 4/12 =1/3 = 0.33 UNR, MATH/STAT 352, Spring 2007

  12. Is a randomly chosen SPADES card a Queen? P(Q|♠) = 1/13 = 0.08 UNR, MATH/STAT 352, Spring 2007

  13. Event of interest: random card is a Queen P(Q) = 4/52 =1/13 ≈ 0.08 Some information does not change the chances for the event: P(Q|red) = 2/26 =1/13 ≈ 0.08 P(Q|♠) = 1/13 = 0.08 … while some does: P(Q|face) = 4/12 =1/3 = 0.33 UNR, MATH/STAT 352, Spring 2007

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