MCA Entrance Previous Year Question Bank

Which of the following statements is not true?

Let $X_1,X_2,\dots ,X_n$ be i.i.d. random variables having pdf f(x) = \frac{1}{\theta} e^{-x/\theta}, \quad 0 < x < \infty,\; \theta > 0 The cdf of the largest order statistic $X_{(n)}=\max (X_1,X_2,\dots ,X_n)$ is:

A discrete random variable X taking non-negative values has the following moment generating function 𝑀_𝑥(t) = 𝑒^{2(𝑒𝑡−1)}; −∞<𝑡<∞ Then, the value of P(X ≤ 1) is:

Let $X$ be a continuous random variable such that E[X] &lt; \infty and $P\left(X\ge \frac{1}{2}+x\right)=P\left(X\le \frac{1}{2}-x\right)$ for all $x\in \mathbb{R}$. Then