QUESTION 2 (TOTAL MARKS: 20) (a) Consider the function fet, 320; 0, otherwise. (i) What properties must have in order to

[answerhappygod]

Question 2 Total Marks 20 A Consider The Function Fet 320 0 Otherwise I What Properties Must Have In Order To 1 (49.37 KiB) Viewed 32 times

QUESTION 2 (TOTAL MARKS: 20) (a) Consider the function fet, 320; 0, otherwise. (i) What properties must have in order to be a valid probability density function? & [2 marks] (ii) Calculate the expected value (mean) and varianco. [3 marks) (iii) Find P(X > 4). [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 iter 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. (6 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 550 or more? (6 marks)