A small technology company is developing a new type of sensor. The company’s engineers are analyzing two key performance characteristics of the sensor: its lifespan and its measurement accuracy. The lifespan, $T$, is the time (in hours) until the sensor fails. The measurement accuracy, $A$, is the absolute difference between the sensor’s reading and the true value (in appropriate units).
b. The engineers collect data on the measurement accuracy, $A$, of a sample of the sensors. They define a new random variable, $C$, where $C = 1$ if $A < 0.5$ (sensor deemed ‘accurate’) and $C = 0$ if $A \ge 0.5$ (sensor deemed ‘inaccurate’).
i. Explain why $C$ is a discrete random variable.
ii. Describe the sample space for the random variable $C$ when four sensors are tested.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 marks, testing your understanding of Random Variables. It falls under Data analysis, probability and statistics in Unit 4: Mathematical Methods Unit 4. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Continues the study of functions, algebra, calculus, and introduces probability and statistics.
Covers discrete and continuous random variables, probability distributions, and statistical inference for sample proportions.
random variables, including the concept of a random variable as a real function defined on a sample space and examples of discrete and continuous random variables
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