QUESTION 2 [TOTAL MARKS: 20 (a) Consider the function f(3) = { . Otherwise 14-1; 0, . (1) What properties must have in o

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Question 2 Total Marks 20 A Consider The Function F 3 Otherwise 14 1 0 1 What Properties Must Have In O 1 (67.01 KiB) Viewed 42 times

QUESTION 2 [TOTAL MARKS: 20 (a) Consider the function f(3) = { . Otherwise 14-1; 0, . (1) What properties must have in order to be a valid probability density function? [2 marks] (ii) Calculate the expected value (mean) and variance. [3 marks] (iii) Find P(X 24). [3 marks) (b) Items from a production line can be classified as either meeting the customer specifica- tions or not meeting customer specifications. The probability that an item meets customer specification is 0.80. Find the probability that exactly 10 ont of the next 15 items produced by the line meet customer specifications, (6 marks) (@) Mathematics Scholastic Aptitude Test (SAT) scores are approximately normally dis- tributed with mean 500 and standard deviation 100, so if X represents a mathematics SAT score, X N(500,100). What is the probability that an individual mathematics SAT score is 550 or more? (6 marks