(a) Consider the function sei, x>0; f(x) = 0, otherwise. (i) What properties must ſ have in order to be a valid probabil

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A Consider The Function Sei X 0 F X 0 Otherwise I What Properties Must S Have In Order To Be A Valid Probabil 1 (35.27 KiB) Viewed 40 times

(a) Consider the function sei, x>0; f(x) = 0, otherwise. (i) What properties must ſ have in order to be a valid probability density function? [2 marks] (ii) Calculate the expcuted value (mean) and variance. [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 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.