Question

Let X be a Gaussian random variable mean 0 and variance ${\sigma }^2.$ Let Y = max(X, 0) where max (a, b) is the maximum of a and b. Th emedian of Y is

• A. 0

Answer 1

The correct option is A 0

1. is Gaussian random variable
   
   $\Rightarrow X\sim N(0,{\sigma }^2)\text{for}-\infty <x<\infty$
   
   Given y = max(x, 0)
   
   $=(\begin{array}{cc}0,& \mathrm{if}-\infty <x\le 0\\ x,& \mathrm{if}0<x<\infty ,\mathrm{is}a\mathrm{random}\mathrm{variable}\end{array}$
   
   $\because$ Median is the centre most value of the distribution so median of y = '0'.