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.
X0123P(X)0.3580.4390.1790.024
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Expert Answer

tabuordg
Answered 2020-11-09 Author has 99 answers
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(X)X×P(X)
=0(0.358)+1(0.439)+2(0.179)+3(0.024)
=0.869
The standard deviation can be calculated as:
Standard deviation (X)=E(X2)(E(X))2
=(X2×P(X))(E(X))2
=((02×0.385)+(12×0.439)++(32×0.024))(0.869)2
=1.3710.755 = 0.785 Thus, the mean and standard deviation are 0.869 and 0.785 respectively.
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