Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Statistics & Exploratory Data Analysis Random Variables & Distribution Functions
Which of the following is a valid cumulative distribution function?
1
F(x) = \(\begin{cases}\rm \frac{1}{2+x^2} & \text { if } \rm x<0, \\\rm \frac{2+x^2}{3+x^2} & \text { if } \rm x \geq 0\end{cases}\)
2
F(x) = \(\begin{cases}\rm\frac{1}{2+x^2} & \text { if } \rm x<0, \\ \rm\frac{2+x^2}{3+2 x^2} & \text { if } \rm x \geq 0\end{cases}\)
3
F(x) = \(\begin{cases}\rm\frac{1}{2+x^2} & \text { if } \rm x<0 \text {, } \\ \rm\frac{2 \cos (x)+x^2}{4+x^2} & \text { if } \rm x \geq 0\end{cases}\)
4
F(x) = \(\begin{cases}\rm\frac{1}{2+x^2} & \text { if } \rm x<0, \\ \rm\frac{1+x^2}{4+x^2} & \text { if } \rm x \geq 0\end{cases}\)
5
Question Not Attempted