The time, $T$ (in minutes), that a customer spends at a particular checkout in a supermarket is a continuous random variable with probability density function given by
$$f(t) = \begin{cases} k(4t - t^2), & 0 \le t \le 4 \ 0, & \text{otherwise} \end{cases}$$
where $k$ is a constant.
a. Find the value of $k$.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 2 marks, testing your understanding of Continuous 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.
continuous random variables: - construction of probability density functions from non-negative functions of a real variable - specification of probability distributions for continuous random variables using probability density functions - calculation and interpretation of mean, $\mu$, variance, $\sigma^{2}$, and standard deviation of a continuous random variable and their use - standard normal distribution, $\mathrm{N}(0,1)$, and transformed normal distributions, $\mathrm{N}\left(\mu, \sigma^{2}\right)$, as examples of a probability distribution for a continuous random variable - effect of variation in the value(s) of defining parameters on the graph of a given probability density function for a continuous random variable - calculation of probabilities for intervals defined in terms of a random variable, including conditional probability (the cumulative distribution function may be used but is not required)
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