Question

3. (9 Marks) The length of time required by students to complete a coe-hour exam is a random variable with a probability density function (pdf) given by 1) = c +2 OSX S1 a) Find the value and write down the new pdf. (2 points) b) Find the probability that a randomly selected student will finish in less than half an hour. (3 points) c) Find the mean and standard deviation of the distribution. (4 points) SD
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Answer 1

f(x) = (a tor? rolne for P.d.f. S files.de, at 'S cotx? dx = 1 [c + 3 اب 1 2 3 - COM = 2.67 O Plosesos) B 8 2 x²+x? da 0 8 20 Y 8 x 0.0625 + 0.125 11 0.125 + 0.083

Elx) S'x. fb). dx 20 1을 x 34 12).da 8 !). 1 + 32+ 15 бо 0.73 12 vlx)= Elx?)- (E\x) Elx2= S'x? f(x) dx for? (2 x 32 12).do 0 8 pe + Ś 58 90 - 0.64 Vlx) Please like 0.64 10.78) 2 0.03 std deviation - Jo.03 0.17 0:17