Answer to Question #179897 in Statistics and Probability for zaimsquah

Question

An independent identically distributed sample size of 3 is chosen from a continuous distribution having density function f(x)=2x,0<x<1, 0 e.w . Find the probability that every member of the sample is less than the median of the distribution.

Answer 1

The probability of a random sample to be less than median $=\frac{1}{2}$ (as 50% values fall below median) therefore probability that all 3 values are below median $=(\frac{1}{2})^3 =\frac{1}{8}$