Let X Be a Continuous Random Variable with a Cumulative $\mathrm { F } ( \mathrm { x } ) = 1 - \mathrm { e } ^ { - \mathrm { x } ^ { 2 } } ( \mathrm { x } \geq 0 )$

Let X be a continuous random variable with a cumulative distribution function $\mathrm { F } ( \mathrm { x } ) = 1 - \mathrm { e } ^ { - \mathrm { x } ^ { 2 } } ( \mathrm { x } \geq 0 )$ . Find $\operatorname { Pr } ( 1 \leq X \leq 2 )$

A) $\mathrm { e } ^ { - 1 }$ - $e ^ { - 4 }$
B) $\mathrm { e } ^ { - 1 }$ - $e ^ { - 2 }$
C) 1 - $\mathrm { e } ^ { - 1 }$ - $e ^ { - 2 }$
D) $\mathrm { e } ^ { - 1 }$ - $e ^ { - 2 }$ - 2
E) none of these

Correct Answer:

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