Find the median (another measure of average) for a random variable with pdf on The median is the 50% mark on probability, that is, the value such that

Question

Find the median (another measure of average) for a random variable with pdf  on  The median is the 50% mark on probability, that is, the value  such that

Quizplus · Accepted Answer

We need to find the value x such that P(X≤x)=0.5. 
Setting the integral equal to 0.5 and solving for x, we get:
 
0.5 = ∫[0,x] 11e^(−t/10) dt 
0.5 = [−110e^(−t/10)]x = −11xe^(−x/10)+11 
11−11xe^(−x/10) = 0.5 
Thus, the solution is approximately x = 6.93. 
The closest option is B) 11eaa948_ccfa_f676_84bc_57af5248e88a_TB2342_11.

Find the Median (Another Measure of Average) for a Random