Standard Normal Distribution
Calculate the probability density function, lower cumulative probability, upper cumulative probability, and inner cumulative probability of the standard normal distribution.
| \(\normalsize Standard\ Normal\ distribution\ N(x)\\ (1) probability\ density\\ \hspace{30px}f(x)={\large\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}}\\ (2) lower\ cumulative\ distribution\\ \hspace{30px}P(x)={\large\int_{\small-\infty}^{\small x}}f(t)dt\\ (3) upper\ cumulative\ distribution\\ \hspace{30px}Q(x)={\large\int_{\small x}^{\small\infty}}f(t)dt\\ (4) inner\ cumulative\ distribution\\ \hspace{30px}I(x)={\large\int_{\small -x}^{\small x}}f(t)dt\\\) |
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