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Tut sol week5

# Tut sol week5 - BES Tutorial Sample Solutions S1/11 WEEK 5...

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BES Tutorial Sample Solutions, S1/11 WEEK 5 TUTORIAL EXERCISES (To be discussed in the week starting March 28) 1. The manager of a factory has determined from past experience that X , the number of repairs required to machines in her factory on any one day, has the following probability distribution: x 0 1 2 3 4 P( X = x ) 0.41 0.25 0.18 0.10 0.06 Calculate the following probabilities: TN: (c) & (d) are not probabilities. Above is a typo. (a) P(1 < X < 4) P(1 < X < 4) = P(X=2)+P(X=3) = 0.18+0.10 = 0.28 (b) P(0 X 3) P(0 X 3) = P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1-P(X=4) = 0.94 (c) ܧሺܺሻ ൌ ߤ ൌ ෍ ݔܲሺܺ ൌ ݔሻ ௔௟௟ ௫ ൌ 0 ൈ 0.41 ൅ 1 ൈ 0.25 ൅ 2 ൈ 0.18 ൅ 3 ൈ 0.1 ൅ 4 ൈ 0.06 ൌ 1.15 (d) ܸܽݎሺܺሻ ൌ ܧሺܺ െ ߤሻ ൌ ߪ ൌ ෍ሺݔ െ ߤሻ ܲሺܺ ൌ ݔሻ ௔௟௟ ௫ ൌ ሺ0 െ 1.15ሻ ൈ 0.41 ൅ ሺ1 െ 1.15ሻ ൈ 0.25 ൅ ሺ2 െ 1.15ሻ ൈ 0.18 ൅ ሺ3 െ 1.15ሻ ൈ 0.10 ൅ ሺ4 െ 1.15ሻ ൈ 0.06 ൌ 1.5075

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2. Suppose that the daily number of errors a randomly-selected teller makes is denoted by X and follows the distribution given in the table below. A human resource manager records the daily numbers of errors of two randomly selected tellers. Denote the associated random variables by X 1 and X 2 . As the selection is random, X 1 and X 2 are independent and follow the same distribution as X . The manager then computes the sample mean ܺ ା௑ where the sample size is n = 2.
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Tut sol week5 - BES Tutorial Sample Solutions S1/11 WEEK 5...

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