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ECE2191 - Probability and AI for engineers - S2 2026
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Which statement best describes an unbiased estimator?
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An engineer wishes to estimate a population mean . Assume independent and identically distributed observations, a known population standard deviation of , and that the sampling distribution of the sample mean is well approximated by a Gaussian distribution. What is the minimum sample size required to estimate with 95% confidence and a maximum margin of error of ?
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Repeated voltage measurements from a sensor are assumed to be independent and identically distributed, with known population standard deviation mV. An engineer averages measurements. What is the standard error of the sample mean? Give your answer in mV. (You only need to provide a numerical value. You do not need to enter the units.)
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In the wireless sensor network scenario introduced in Question 1, when applying the Central Limit Theorem, which quantity would the communications engineer standardise to compute a -score?
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Continuing with the wireless sensor network scenario introduced in Questions 1 to 3, suppose the -score corresponding to an observed sample packet-loss rate is . Using a -table, estimate the probability that the sample packet-loss rate is less than or equal to the aforementioned observed sample packet-loss rate. (Input your answer as a decimal rather than a fraction, and include at least 2 decimal places.)
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A communications engineer is testing a wireless sensor network. During testing,
packets are transmitted from a sensor to a gateway. Define
Assume the
are independent and identically distributed (IID) Bernoulli random variables with packet-loss probability. The engineer computes the sample packet-loss rate
Which statement best describes the Law of Large Numbers?
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Continuing with the wireless sensor network scenario introduced in Questions 1 and 2, suppose the packet-loss probability is . A test transmits packets. Using the Central Limit Theorem, the sample packet-loss rate may be approximated as Gaussian. What is the -score corresponding to an observed sample packet-loss rate of 0.08? (Input your answer as a decimal rather than a fraction, and include at least 2 decimal places.)
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Which of the following are examples of real-world behaviour where the assumption 'all memory cell defects occur independently' likely fails to hold. Select ALL examples that apply.
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A digital circuit contains 8 identical logic gates. Each gate fails independently with probability . Let be the number of failed gates. Find the probability that exactly 2 gates fail. (Input your answer as a decimal rather than a fraction, and include at least 2 decimal places.)
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A chip has 50 memory cells. Each memory cell is defective with probability 0.02. What is the expected number of defective cells on the chip? (Input your answer as a decimal rather than a fraction, and include at least 2 decimal places.)
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