# GATE2015-40

For a discrete random variable $X$, $\textit{ran}(X)=\{0,1,2,3\}$ and the cumulative probability $F(X )$ is shown below: $$\begin{array}{|c|c|c|c|c|} \hline X & 0 & 1 & 2 & 3 \\ \hline F(X) & 0.5 & 0.6 & 0.8 & 1.0 \\ \hline \end{array}$$The mean value of $X$ is ___________

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## Related questions

1
If the values of two random variables $(X,Y)$ are $(121, 360)$, $(242, 364)$ and $(363, 362)$, the value of correlation coefficient between $X$ and $Y$ (rounded off to one decimal place) is ________.
2
The median value for the dataset $\left ( 12, 10,16,8,90,50,30,24 \right )$ is ______________.
A normal random variable has mean equal to $0$, and standard deviation equal to $3$. The probability that on a random draw the value of this random variable is greater than $0$ is __________ (round off to $2$ decimal places).
Runs scored by a batsman in five one-day matches are $55$, $75$, $67$, $88$ and $15$. The standard deviation is _________
For the probability density $P(x) = 0.5e^{-0.5x}$, the integral $\displaystyle \int_0^{\infty}P(x)dx =$ __________