7. A random variable, X, has the following cumulative distribution function. if x < 1 of F(X)= X²-2X+5 8 F(x)= x² - 2x+5

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7 A Random Variable X Has The Following Cumulative Distribution Function If X 1 Of F X X 2x 5 8 F X X 2x 5 1 (166.39 KiB) Viewed 20 times

Please notice the correct answer is e. Please ignore my wrong process. And I need detailed solving process. Thank you!!!!
7. A random variable, X, has the following cumulative distribution function. if x < 1 of F(X)= X²-2X+5 8 F(x)= x² - 2x+5 8 if 1 < x <3 = 1,2² if 3 ≤ x 8x² *x + { = {x²-3x+5 f(x) = 3x - 4 = £x-4 Calculate the variance of X. (a) 2.82 (b) 2.07 E[x] = [²³ (7x- #) x dx = 1²³ #x²- 4x dx 2014 (= ² - ² ² = (³- 70)²-(3-0)-7 1.48 (d) 1.18 0.56 (@90* [[x²] = {(³ (£x- $)x³dx = [² #x²³ + x² de [3]+([k]) - ૮ ।+]?? = 7x²1x²1²= 10²-10³² (1-4)= 4 ² 1 deviations e