Question 2 Total Marks 201 N Consider The Function 0 Otherwise 1 What Properties Must Have In Order To Be A Valid 1 (42.15 KiB) Viewed 43 times
Question 2 Total Marks 201 N Consider The Function 0 Otherwise 1 What Properties Must Have In Order To Be A Valid 2 (55.41 KiB) Viewed 43 times
QUESTION 2 TOTAL MARKS: 201 (n) Consider the function 0, otherwise (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(X4) (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 out of the next 15 items produced by the line meet customer specifications. 16 marks (c) 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 350 or more? [6 marks
QUESTION 1 [TOTAL MARKS: 20 (a) Events A and B in a sample space have P(A) = 4, P(B) = f and P(AUB) = (1) Find P(ANB). (ii) Find P(AB). (iii) Find P(BA). (iv) Are A and B independent? Why or why not? (5 marks! (b) The probability that a certain beginner at golf gets a good shot if he uses the correct club is, and the probability of a good shot with an incorrect club is $. In his bag are 5 different clubs, only one of which is correct for the shot in question. If he chooses a club at random and takes a stroke, what is the probability that he gets a good shot? [10 marks) (e) In part (b), if it is known that a good shot has resulted, what is the probability that the right club was used? (5 marks! TIMIC RLLUTLU. ZTTOOS D FOCUS le tv 26 ICD 0
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