5(a) Let X denote a uniform random variable model in the interval [α, β] given by
1
𝑓(𝑥) = {
⁄
(𝛽 − 𝛼)
, 𝛼≤𝑥≤𝛽 0, 𝑜𝑡h𝑒𝑟𝑤𝑖𝑠𝑒 .
AP[4]
5
(i) Show that the 𝑆𝐷(𝑋) = (𝛽−𝛼) CR [6] 2√3
(ii)explain your results with respect to the given uniform random variable model, CR [4]
(b) Use Matlab to plot and simulate the function 𝑈 = 2 log10(60𝑥 +
1) 𝑎𝑛𝑑 𝑉 = 3 cos(6𝑥), over the interval 0 ≤ 𝑥 ≤ 2. Properly label
the plot on each curve. The variable 𝑈 𝑎𝑛𝑑 𝑉 represents speed in miles per hour, the variable 𝑥 represent distance in miles. EV [4]
(c) Use Matlab to plot the function 𝑇 = 8𝑙𝑛𝑡 − 5𝑒0.3𝑡, over the interval
1 ≤ 𝑡 ≤ 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]
(d)Suppose 𝑥 takes on the values 𝑥 = 1, 1.2, 1.4, ... ,5. Use matlab to simulate and compute the array Y that result from the function Y=6sin(5x
