Probability Distribution of a Random Variate

A continuous random variable X has probability distribution function $f\left(x\right)=3x^2, 0\le x\le 1$, then the value of $a$ and $b$ such that $P\left(X\le a\right)=P\left(X>a\right)$

If the probability density function of a random variable is given by $f\left(x\right)=\left\{\begin{array}{l}k\left(1-x^2\right), 0<x<1\\ 0, \text{elsewhere}\end{array}\right.$, then the value of $k$ is

The total lifetime (in year) of $5$ year old dog of a certain breed in a random variable whose distribution function is given by $f\left(x\right)=\left\{\begin{array}{ll}0& , \text{for} x\le 5\\ 1-\frac{25}{x^2},& \text{for} x>5\end{array}\right.$. Then the probability that such a five-year-old dog will live beyond $10$ years are

If $F\left(x\right)=\frac{1}{\mathrm{\pi }}\left(\frac{\mathrm{\pi }}{2}+{\tan }^{-1}\right)-\infty <x<\infty$ is a distribution function of a continuous variable $X,$ then $P\left(0\mathit{\le }x\mathit{\le }1\right)$ is

For the probability density function $f\left(x\right)=\left\{\begin{array}{lr}2e^{-2x},& x>0\\ 0,& x\le 0\end{array}\right.$

$F\left(2\right)$ is equal to