Question
2. Assume that if a certain scale in a laboratory has been used too long without recalibration the
probability density function of the measurement error is f(x) = 1 – 0.5x for 0<x (mg) <2.0.
a. If a measurement error within 0.5 mg is acceptable, what is the probability that an error is
not acceptable before calibration?
b. What is the value of measurement error exceeded with probability 0.2 before calibration?
c. What is the probability that the measurement error is exactly 0.22 mg before calibration?
d. Which of the following expressions is appropriate for the cumulative distribution
function for this variable in the range 0<x (mg)< 2.0?
(a) F(x) = x -- 0.25x²
(b) F(x) = x - 0.125x²
(c) F(x) = x – 0.5x²
(d) None of the other answers is correct
e. What is the mean value of the random variable in this problem?
f. What is the variance of the random variable in this problem?
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Transcribed Image Text

2. Assume that if a certain scale in a laboratory has been used too long without recalibration the probability density function of the measurement error is f(x) = 1 – 0.5x for 0<x (mg) <2.0. a. If a measurement error within 0.5 mg is acceptable, what is the probability that an error is not acceptable before calibration? b. What is the value of measurement error exceeded with probability 0.2 before calibration? c. What is the probability that the measurement error is exactly 0.22 mg before calibration? d. Which of the following expressions is appropriate for the cumulative distribution function for this variable in the range 0<x (mg)< 2.0? (a) F(x) = x -- 0.25x² (b) F(x) = x - 0.125x² (c) F(x) = x – 0.5x² (d) None of the other answers is correct e. What is the mean value of the random variable in this problem? f. What is the variance of the random variable in this problem?

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