After manufacture, computer disks are tested for errors. Let X be the number of

Question

After manufacture, computer disks are tested for errors. Let X be the number of errors detected on a randomly chosen disk. The following table presents values of the cumulative distribution function F(x) of X. What is the probability that two or fewer errors are detected? What is the probability that more than three errors are detected? What is the probability that exactly one error is detected? What is the probability that no errors are detected? What is the most probable number of errors to be detected?

Explanation / Answer

We are given the cumulative distribution function. i.e we are given P(X<=x)
------------------------------------------------------------------------------------------------- a)P( two or fewer errors are detected)=P(X<=2)                                                         =0.83 -------------------------------------------------------------------------------------------------- b) P(more than 3 errors are detected)=P(X>3)                                                       =1-P(X<=3)                                                       =1-0.95                                                       =0.05 ------------------------------------------------------------------------------------------------- c) P(exactly one error is detected)=P(x=1)                                                   =P(x<=1)-P(x<=0)                                                   =0.72-0.41                                                   =0.31 -------------------------------------------------------------------------------------------------- d)P(no error is detected)=P(X=0)                                    =P(X<=0)                                    =0.41 ------------------------------------------------------------------------------------------------- e) Since the probability corresponding to x=0 is highest(0.41), most probable number of errors=0 -------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------

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