mid-2 - CS 3341 (Dr. Baron) Anti-Midterm (SOLUTIONS) Solve...

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CS 3341 (Dr. Baron) Anti-Midterm (SOLUTIONS) Solve any 3 of the following 4 problems. Each problem worth 20 pts. Time: 1 hour 15 minutes. This is an open-book, open-notes test. Calculators are allowed. 1. The time, in minutes, it takes to reboot a certain system is a continuous variable with the density f ( x ) = ( C (10 - x ) , if 0 < x < 10 0 , otherwise (a) Compute C . (b) Compute the probability that it takes more than 6 minutes to reboot the system. SOLUTION. ( a ) Z f ( x ) dx = Z 10 0 C (10 - x ) dx = - C (10 - x ) 2 2 x =10 x =0 = - C 0 - 100 2 = 50 C = 1 , therefore, C=0.02 . ( b ) P { X > 6 } = Z 10 6 f ( x ) dx = Z 10 6 0 . 02(10 - x ) dx = - 0 . 02 (10 - x ) 2 2 x =10 x =6 = - 0 . 02 0 - 16 2 = 0.16 2. Before the computer is assembled, its vital component (motherboard) goes through a special inspection. Only 80% of components pass this inspection. (a) What is the probability that at least 18 of the next 20 components pass in- spection? (b) What is the probability that at least 180 of the next 200 components pass
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mid-2 - CS 3341 (Dr. Baron) Anti-Midterm (SOLUTIONS) Solve...

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