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M i d t e r m - E N G R 371 - February 1997

Pens, pencils, erasers, and straight edges only. No calculators. No crib sheets.
   If you have a difficulty you may try making REASONABLE assumptions. State
the assumption and how that assumption limits your answer. Justify your responses.

  1. An electronic assembly consists of two subsystems say A and B. From previous
     testing procedures, the following probabilities are assumed to be known:
     P ( A fails) = 0.2
     P(B fails and A doesn't fail) = 0.15
     P(both A and B fail) = 0.15
     Evaluate the following:

      (a) P ( A fails|B has failed).
      (b) P ( A fails and B doesn't fail).

     (Total 7 marks)

  2. Let X denote the thrust and Y denote the mixture ratio, which are two ma-
     jor characteristics of rocket engine's performance. Suppose that X and Y are
     continuous random variables with joint probability distribution function:




      (a) Find k.
      (b) Determine whether X and Y are independent.
      (c) Compute P{X      <       Y=).

     (Total 9 marks)

  3. The total time, measured in units of 100 hours that an Arts and Science student
     runs his/her stereo over a period of one year is a continuous R.V. X with pdf

                                              x     0< x < 1
                                   f(x)   = < 2-x   l<x    <2
                                              0     otherwise

      (a) Determine EX
      (b) Determine the variance of X.
      (c) Define Y = QOX + 30X. Determine the mean of Y.
                               2




      (d) Determine the variance of Y.

     (Total 9 marks)
     (Exam Total 25 marks)
Some Useful Equations



               P(fjb              ~ka<X</j,-{-ka)>l-^-
                                                    k                                      2


                                              n                    j_

                                            i=l                        z




                                             >        Tl
                                                               =




                                                                                       e
                                                               i=0



                               /(*) = [ " J P V ^
                            /(*) = ( * 11 ) PNT*
                                                      f(x)=pq -            x 1




                                            / ( * )        =                           ^



                              / ( * )        =                                   2.2



                        J     x - e- dx
                               a l      x
                                                               = (a-               1)!

                                                      ./           x         1 =a

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Engr 371 midterm february 1997

  • 1. M i d t e r m - E N G R 371 - February 1997 Pens, pencils, erasers, and straight edges only. No calculators. No crib sheets. If you have a difficulty you may try making REASONABLE assumptions. State the assumption and how that assumption limits your answer. Justify your responses. 1. An electronic assembly consists of two subsystems say A and B. From previous testing procedures, the following probabilities are assumed to be known: P ( A fails) = 0.2 P(B fails and A doesn't fail) = 0.15 P(both A and B fail) = 0.15 Evaluate the following: (a) P ( A fails|B has failed). (b) P ( A fails and B doesn't fail). (Total 7 marks) 2. Let X denote the thrust and Y denote the mixture ratio, which are two ma- jor characteristics of rocket engine's performance. Suppose that X and Y are continuous random variables with joint probability distribution function: (a) Find k. (b) Determine whether X and Y are independent. (c) Compute P{X < Y=). (Total 9 marks) 3. The total time, measured in units of 100 hours that an Arts and Science student runs his/her stereo over a period of one year is a continuous R.V. X with pdf x 0< x < 1 f(x) = < 2-x l<x <2 0 otherwise (a) Determine EX (b) Determine the variance of X. (c) Define Y = QOX + 30X. Determine the mean of Y. 2 (d) Determine the variance of Y. (Total 9 marks) (Exam Total 25 marks)
  • 2. Some Useful Equations P(fjb ~ka<X</j,-{-ka)>l-^- k 2 n j_ i=l z > Tl = e i=0 /(*) = [ " J P V ^ /(*) = ( * 11 ) PNT* f(x)=pq - x 1 / ( * ) = ^ / ( * ) = 2.2 J x - e- dx a l x = (a- 1)! ./ x 1 =a