Consider randomly selecting a point (x1, x2, x3) in the unit cube {(x1, x2, x3): 0 < x1 < 1, 0 < x2 < 1, 0 < x3 < 1}according to the joint pdf fðx1; x2; x3þ ¼ 8x1x2x3 0 < x1 < 1; 0 < x2 < 1; 0 < x3 < 1 0 otherwise ( (so the three variables are independent). then form a rectangular solid whose vertices are (0, 0, 0), (x1, 0, 0), (0, x2, 0), (x1, x2, 0), (0, 0, x3), (x1, 0, x3), (0, x2, x3), and (x1, x2, x3). the volume of this cube is y3 ¼ x1x2x3. obtain the pdf of this volume. [hint: let y1 ¼ x1 and y2 ¼ x1x2.]

answer: -2+√x,-2-√x

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1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours