Two numbers are chosen independently and uniformly at random from the set {1, 2, ...., 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ______.

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

A probability density function on the interval $$\left[ {a,1} \right]$$ is given by $$1/{x^2}$$ and outside this interval the value of the function is zero. The value of $$a$$ is _________.