Question

X P(x) 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. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Does the table show a probability distribution? Select all that apply. 0 1 2 3 0.363 0.437 0.179 0.021 A. Yes, the table shows a probability distribution B. No, the random variable x is categorical instead of numerical. c. No, the sum of all the probabilities is not equal to 1. OD. No, not every probability is between 0 and 1 inclusive. E. No, the random variable x's number values are not associated with probabilities.

Answer 1

Yes. The table shows a probability distribution- Because every probability is between o and 1 inclusive and Sum of all probabilities equal to one- Mean, M= E(X) = {x. p(x) = Cox 0.363) + (1x0.437) + (2x0.179) + (3x 0.021) ie M = 0.9 e ECx®) - Expex) (0²x0.363) + (1x0.437) + (2²x0.179) + ( 3² x 0-oal) = 1.342 :: v(x) = ² = E(X²) - [[(x)]² 1.342 - 0.9) 2 = 0.532 10.532 0.