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GATE2019: 49

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A new game is being introduced in a casino. A player can lose Rs. $100$, break even, win Rs. $100$, or win Rs. $500$. The probabilities $(P(X))$ of each of these outcomes $(X)$ are given in the following table:

$$\begin{array}{|cl|cI|cI|cI|cI|c|}\hline
&\text{X (in Rs.)} & \text{-100} & \text{0} & \text{100} & \text{500}  \\ \hline &\text{P (X)} & \text{0.25} & \text{0.5} & \text{0.2} & \text{0.05} \\ \hline \end{array}$$

The standard deviation ($\sigma$) for the casino payout is Rs. _____________ (rounded off to the nearest integer).

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