GATE Civil Engineering
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If $\{x\}$ is a continuous, real valued random variable defined over the interval $(- \infty, + \infty)$ and its occurrence is defined by the density function given as: $f(x) = \dfrac{1}{\sqrt{2 \pi} *b} e^{-\frac{1}{2} (\frac{x-a}{b})^2}$ where $’a’$ and $b’$ are the statistical attributes of the random variable $\{x\}$. The value of the integral $\int_{- \infty}^{a} \dfrac{1}{\sqrt{2 \pi}*b} e^{-\frac{1}{2} (\frac{x-a}{b})^2} dx$ is

  1. $1$
  2. $0.5$
  3. $\pi$
  4. $\dfrac{\pi}{2}$
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