Solution Found!
Determine the cumulative distribution function
Chapter 4, Problem 31E(choose chapter or problem)
Determine the cumulative distribution function for the random variable in Exercise 4-13.
4-13.A test instrument needs to be calibrated periodically to prevent measurement errors. After some time of use without calibration. It is known that the probability density function of the measurement error is \(f(x)=1-0.5 x\) for 0 < x < 2 millimeters.
If the measurement error within 0.5 millimeters is acceptable, what is the probability that the error is not acceptable before calibration?What is the value of measurement error exceeded with probability 0.2 before calibration?What is the probability that the measurement error is exactly 0.22 millimeters before calibration?Equation transcription:
Text transcription:
f(x)=1-0.5 x
Questions & Answers
QUESTION:
Determine the cumulative distribution function for the random variable in Exercise 4-13.
4-13.A test instrument needs to be calibrated periodically to prevent measurement errors. After some time of use without calibration. It is known that the probability density function of the measurement error is \(f(x)=1-0.5 x\) for 0 < x < 2 millimeters.
If the measurement error within 0.5 millimeters is acceptable, what is the probability that the error is not acceptable before calibration?What is the value of measurement error exceeded with probability 0.2 before calibration?What is the probability that the measurement error is exactly 0.22 millimeters before calibration?Equation transcription:
Text transcription:
f(x)=1-0.5 x
ANSWER:Step 1 of 2
The probability density function of the measurement of error given in Exercise 4-13 is,
The cumulative distribution function of a continuous random variable X is,
