Merkpositionering

Faisal Shahzad, 30, a United States naturalized citizen from Pakistan, pleaded guilty to a failed attempt to explode a car bomb in Times Square in New York City in May 2010. Shahzad was sentenced to life in prison. (Songquan Deng/Shutterstock.) $z ‐ value 1.645$ Faisal Shahzad, 30, a United States naturalized citizen from Pakistan, pleaded guilty to a failed attempt to explode a car bomb in Times Square in New York City in May 2010. Shahzad was sentenced to life in prison. (Songquan Deng/Shutterstock.)

P (ppf) = (0.8) (0.8) (0.2) = 0.128

\begin{matrix} (1) f (x_{i}) \geq 0 \\ (2) \sum_{i = 1}^{n} f (x_{i}) = 1 \\ (3) f (x_{i}) = P (X = x_{i}) \end{matrix}

f (x) = \{0.038, x = 1 0.102, x = 2 0.172, x = 3 0.204, x = 4 0.174, x = 5 0.124, x = 6 0.080, x = 7 0.036, x = 8 0.028, x = 9 0.022, x = 10 0.020, x = 15

Formula 1: $$ \begin{equation} \label{Formula1.Label} P (\Omega) = \int_{-\infty}^{+\infty} f (x) \: dx = 1 \end{equation} $$

Formula 2: $$ \begin{equation} \label{Formula2.Label} E (X) := \int_{-\infty}^{+\infty} x \: f (x) \; dx \end{equation} $$

A third one, with references to 1 and 2: $$ \begin{equation} \begin{array}{ll} E (a X + b) & = \int_{-\infty}^{+\infty} (a x - b) \: f(x) \: dx \\ \\ & = a \int_{-\infty}^{+\infty} x \: f(x) \: dx + b \int_{-\infty}^{+\infty} f(x) \: dx \\ \\ & \underset{\eqref{Formula1.Label}, \eqref{Formula2.Label}}{=} a E(X) + b \end{array} \end{equation} $$

And another one: $$ \begin{equation} V(X) = \frac{a^2 + b^2 + c^2 - ab - ac - bc}{18} \end{equation} $$