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{"ops":[{"insert":"5(a) Let X denote a uniform random variable model in the interval [\u03b1, \u03b2] given by\n1\n\ud835\udc53(\ud835\udc65) = {\n\u2044\n(\ud835\udefd \u2212 \ud835\udefc)\n, \ud835\udefc\u2264\ud835\udc65\u2264\ud835\udefd 0, \ud835\udc5c\ud835\udc61h\ud835\udc52\ud835\udc5f\ud835\udc64\ud835\udc56\ud835\udc60\ud835\udc52 .\nAP[4]\n5\n\n (i) Show that the \ud835\udc46\ud835\udc37(\ud835\udc4b) = (\ud835\udefd\u2212\ud835\udefc) CR [6] 2\u221a3\n(ii)explain your results with respect to the given uniform random variable model, CR [4]\n(b) Use Matlab to plot and simulate the function \ud835\udc48 = 2 log10(60\ud835\udc65 +\n1) \ud835\udc4e\ud835\udc5b\ud835\udc51 \ud835\udc49 = 3 cos(6\ud835\udc65), over the interval 0 \u2264 \ud835\udc65 \u2264 2. Properly label\nthe plot on each curve. The variable \ud835\udc48 \ud835\udc4e\ud835\udc5b\ud835\udc51 \ud835\udc49 represents speed in miles per hour, the variable \ud835\udc65 represent distance in miles. EV [4]\n(c) Use Matlab to plot the function \ud835\udc47 = 8\ud835\udc59\ud835\udc5b\ud835\udc61 \u2212 5\ud835\udc520.3\ud835\udc61, over the interval\n1 \u2264 \ud835\udc61 \u2264 3 . Put a title on the plot and properly label the axes. The variable T represents temperature in degree Celsius, the variable t represent time in minutes. CR [4]\n(d)Suppose \ud835\udc65 takes on the values \ud835\udc65 = 1, 1.2, 1.4, ... ,5. Use matlab to simulate and compute the array Y that result from the function Y=6sin(5x\n"}]}

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