Find the median of x, rounded to three decimal places, given the pdf , . [Hint: Do not waste time trying to find an analytic solution. Once you determine the expression you would like to solve, just identify which of the choices is close to the correct answer.]
A) 3.000
B) 0.420
C) 0.559
D) 6.713

Question

Find the median of x, rounded to three decimal places, given the pdf  ,  . [Hint: Do not waste time trying to find an analytic solution. Once you determine the expression you would like to solve, just identify which of the choices is close to the correct answer.]
A) 3.000 
B) 0.420 
C) 0.559 
D) 6.713

Quizplus · Accepted Answer

To find the median, we need to solve for x in the equation:
0.5 = ∫ from -∞ to x (2t-1) dt
Simplifying,
0.5 = [t^2 - t] from -∞ to x
0.5 = x^2 - x + 0.5
x^2 - x = 0
x(x-1) = 0
x = 0 or x = 1
Since the pdf is symmetric around x=0.5, the median is also at x=0.5. Option C, which is the closest to 0.5, is the correct answer.

Find the Median of X, Rounded to Three Decimal Places