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ECE2191 - Probability and AI for engineers - S2 2026

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Each packet transmission attempt succeeds independently with probability . Let denote the number of attempts up to, and including, the first success. The first five attempts have failed. What is the probability that more than three additional attempts are required before the first success?
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Two zero-mean Gaussian noise sources and have different standard deviations. An engineer observes that . Which conclusion is valid?
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An engineer constructs a 95% confidence interval for the population mean and obtains . Which statement is correct?
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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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