$$\mathop {\lim }\limits_{t \to + \infty } \sqrt{t^2+t}-t= $$

(Round

off to one decimal place)

Let $Y=Z^2, Z=\frac{X-\mu}{\sigma}$, where $X$ is a normal random variable with mean $\mu$ and variance $\sigma^2$. The variance of $Y$ is

Let $A \in \mathbb{R}^{n \times n}$ be such that $A^3=A$. Which one of the following statements is ALWAYS correct?

Consider the cumulative distribution function (CDF) of a random variable X :

$$ F_X(x)=\left\{\begin{array}{cc} 0 & x \leq-1 \\ \frac{1}{4}(x+1)^2 & -1 \leq x \leq 1 \\ 1 & x \geq 1 \end{array}\right. $$

The value of $P\left(X^2 \leq 0.25\right)$