1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability Homework Help

  1. Aug 30, 2011 #1
    The following table gives the probability distribution of X, the number of defective products in a production line in a day.
    x P(X=x)

    0 0.04

    1 0.19

    2 0.35

    3 0.26

    4 0.16

    a. Evaluate P(|X - expected value| >= standard dev)
    b. The cost of maintaining the machine at the production line is given by C = 50 + 3x + 2x^2. Find the mean maintaining cost.
     
    Last edited: Aug 30, 2011
  2. jcsd
  3. Aug 30, 2011 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Show your work. What have you done so far? Where are you stuck?

    RGV
     
  4. Aug 30, 2011 #3
    I only managed this much:

    Expected value = 2.31
    Standard deviation = 1.074

    P( |X - 2.31| >= 1.074)
    =P( -1.074 >= (X - 2.31) >= 1.074 )
    =P( 1.236 >= X >= 3.384)

    I'm stuck here. For question b, I assume I have to calculate the expected value of C by substituting the variables x and x^2 with their respective expected values?
     
  5. Aug 31, 2011 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    This doesn't make sense since 1.236 clearly isn't less than or equal to 3.384.

    The condition |X - 2.31| ≥ 1.074 is equivalent to (X-2.31 ≥ 1.074) or (X-2.31 ≤ -1.074), so
    [tex]P(\lvert X-2.31 \rvert \ge 1.074) = P(X-2.31 \ge 1.074) + P(X-2.31 \le -1.074)[/tex]
    Yes, because E(C) = E(50 + 3x + 2x^2) = E(50) + E(3x) + E(2x2) = 50 + 3 E(x) +2 E(x2)
     
  6. Aug 31, 2011 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    |X - 2.31| >= 1.074 <--> either X - 2.31 >= 1.074 or 2.31 - X >= 1.074.

    RGV
     
  7. Aug 31, 2011 #6
    So is this how it goes, based on the given values of x and P(X=x):

    P(|X-2.31| >= 1.074)
    = P( X-2.31 >= 1.074) + P( 2.31-X >= 1.074)
    = P( X >= 3.384) + P( X <= 1.236)
    = 0.16 + 0.19 + 0.04
    = 0.39
     
  8. Sep 1, 2011 #7

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Yes, that's right.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Probability Homework Help
Loading...