1. Suppose it's a bad year and COVID-19 has mutated, the borders are all closed and there are only 60 students enrolled

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1 Suppose It S A Bad Year And Covid 19 Has Mutated The Borders Are All Closed And There Are Only 60 Students Enrolled 1 (93.47 KiB) Viewed 118 times

1. Suppose it's a bad year and COVID-19 has mutated, the borders are all closed and there are only 60 students enrolled in FIT5197 for 2021 Semester 1. The final exam marks are distributed as per a Gaussian distribution, Ś ~ N(u = 110, 02 = 102). Given P(100 < <110) = 0.35, how many students will get at least 120 marks? 2. You are building a spectacular rocket ship to fly into outer space. Assume the fuel meter can be modelled as a unitless linear system y = I1 + 12 + €, where x1 and 22 are 2 different and independent states of the system and e is a Gaussian white noise terme~ N(0,1). We know that I 1 ~ N(u = 1,62 = 2), 22 ~ N(u = 2,6= 4). Find the distribution of y and calculate what the probability is when y > 3? 3. On the eve of the holidays, you are going to hang two strings of colorful lights on the tree in front of your house. The first flashing of the two strings of colored lights are independent of each other, and may occur at any time uniformly within 4 seconds after power-on, and then each string of colored lights flashes at an interval of 4 seconds. If the two strings of colored lights are energized at the same time, what is the probability that the difference between their first flashing moments is no more than 2 seconds? 4. A random variable X is distributed as a uniform distribution X ~ U[2,5). Now we get 3 independent observations, what is the probability that at least 2 observations greater than 3?