 # Self-Driving Vehicle Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say tinfoQ 2020-11-08 Answered
Self-Driving Vehicle Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a self-driving vehicle Consider, X be the random variable that represents the number if adults who feel comfortable in a self-driving vehicle.
$\begin{array}{|ccccc|}\hline X& 0& 1& 2& 3\\ P\left(X\right)& 0.358& 0.439& 0.179& 0.024\\ \hline\end{array}$
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A probability distribution function must satisfy the following conditions:
Sum of probabilities must be equal to 1.
Probabilities must lie between 0 and 1.
Here, conditions required for a probability distribution are satisfied because probabilities are between 0 and 1 and sum of probabilities is equal to 1 which can be shown as:
Sum of probabilities $=0.358+0.439+0.179+0.024=1$
Since, both the conditions for a probability distribution function are satisfied, the mean for the provided distribution can be calculated as: $E\left(X\right)\sum X×P\left(X\right)$
$=0\left(0.358\right)+1\left(0.439\right)+2\left(0.179\right)+3\left(0.024\right)$
$=0.869$
The standard deviation can be calculated as:
Standard deviation $\left(X\right)={\sqrt{E\left({X}^{2}\right)-\left(E\left(X\right)\right)}}^{2}$
$={\sqrt{\sum \left({X}^{2}×P\left(X\right)\right)-\left(E\left(X\right)\right)}}^{2}$
$=\sqrt{\left(\left({0}^{2}×0.385\right)+\left({1}^{2}×0.439\right)+\dots +\left({3}^{2}×0.024\right)\right)-{\left(0.869\right)}^{2}}$
$=\sqrt{1.371-0.755}$ = 0.785 Thus, the mean and standard deviation are 0.869 and 0.785 respectively.