2probabilitydistribution-210511123456.pptx

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1. Probability Distribution of a Random Variable

2. PROBABILITY DISTRIBUTION the set of all possible values of the random variable X, together with their corresponding associated probabilities .

3. PROBABILITY DISTRIBUTION (𝑅𝑎𝑛𝑑𝑜𝑚 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑋) 𝐴𝑔𝑒 𝑃(𝑥) 16 6/25 17 14/25 18 5/25

4. PROBABILITY DISTRIBUTION If X is a discrete random variable , the probability distribution is called a probability mass function or pmf. The pmf may be expressed in tabular or graphical form.

5. Properties of a Probability Distribution I. ≤ 𝑃 𝑥 ≤ 1 2. Σ𝑃 𝑥 = 1

6. discrete probability distribution or not? x 1 2 3 4 5 P(x) 0.10 0.20 0.25 0.40 0.05

7. discrete probability distribution or not? x 1 2 3 4 5 P(x) 0.05 0.25 0.33 0.25 0.08

8. discrete probability distribution or not? x 1 2 3 4 P(x) 0.2 0.1 0.4 0.3

9. discrete probability distribution or not? x 1 2 3 4 P(x) 0.2 0.1 0.4 0.3 Determine 𝑃 1 + 𝑃 2 : 0.2 + 0.1 = 0.3

10. discrete probability distribution or not? Determine 𝑃 3 − 𝑃 1 : 0.4 − 0.2 = 0.2 x 1 2 3 4 P(x) 0.2 0.1 0.4 0.3

11. discrete probability distribution or not? Determine P(4)+P(2). x 1 2 3 4 P(x) 0.2 0.1 0.4 0.3

12. The spinner below is divided into 12 sections. Let X be the score where the arrow will stop (numbered as 1, 2, 3, 4, 5). Find the probability that the arrow will stop at 1, 2, 3, 4, and 5. Construct the discrete probability distribution of the random variable X and its corresponding histogram.

13. Suppose three cell phones are tested at r ando m . W e want to find out the number of defective cell phones that occu r . Th u s , to each outcome in the sample space we shall assign a value.These are 0, 1, 2, or 3. If there is no defective cell phone, we assign the number 0; if there is one defective cell phone, we assign the number 1; if there are two defective cell phones, we assign the number 2; and 3, if there are three defective cell phones.The number of defective cell phones is a random variable.The possible values of this random variable are 0,1,2, and 3.

14. Let D = defective CP N = non- defective CP X = ( the random variable) number of defective cell phones Possible Outcomes Value of the Random Variable X ( number of defective cell phones ) DDD 3 DDN 2 DND 2 DNN 1 NNN NND 1 NDN 1 NDD 2

15. 𝑋 number of defective cell phones 𝑃(𝑥) 3 1 8 2 3 8 1 3 8 1 8 Possible Outcomes Value of the Random Variable X ( number of defective cell phones ) DDD 3 DDN 2 DND 2 DNN 1 NNN NND 1 NDN 1 NDD 2

16. 𝑋 number of defective cell phones 𝑃(𝑥) 3 1 8 2 3 8 1 3 8 1 8 8 8 7 8 6 8 5 8 4 8 3 8 2 8 1 8 1 2 3

17. Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Find the values of the random variable Z.

18. Possible Outcomes Value of the Random Variable Z (number of blue balls) 𝑍 number of blue balls 𝑃(𝑧)

19. 𝑍 number of blue balls 𝑃(𝑧)

20. A shipment of five boxes of mussels (tahong) contains two that are slightly spoiled. If a retailer receives three of these boxes of mussels at random, list the elements of the sample space using the letters S and F for spoiled and fresh mussels, r esp e c t i v e l y . T o each sample point, assign a value x of the random variable X representing the number of boxes of mussels purchased by the retailer which are slightly spoiled.

21. 𝑋 number of boxes of mussels which are slightly spoiled 𝑃(𝑥) Possible Outcomes Value of the Random Variable X ( number of boxes of mussels which are slightly spoiled )

22. 𝑋 number of boxes of mussels which are slightly spoiled 𝑃(𝑥)