The county highway department recorded the following probabilities for the number of accidents per day on a certain freeway for one month. The number of accidents per day and their corresponding probabilities are shown. (Round your answers to three decimal places if needed.) Number of accidents, X 0 1 2 3 4 Probability P(X ) 0.4 0.2 y 0.2 0.1 Find y so that this is a valid probability distribution. Find the mean of this distribution using the value found for y in part a. Find the expected value of number of accidents per day. The variance and standard deviation of this distribution using the value found for y in part a are respectively , ________and _________.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The county highway department recorded the following probabilities for the number of accidents per day on a certain freeway for one month. The number of accidents per day and their corresponding probabilities are shown. (Round your answers to three decimal places if needed.)
| Number of accidents, X | 0 | 1 | 2 | 3 | 4 |
| 0.4 | 0.2 | y | 0.2 | 0.1 |
- Find y so that this is a valid probability distribution.
- Find the mean of this distribution using the value found for y in part a.
- Find the
expected value of number of accidents per day. - The variance and standard deviation of this distribution using the value found for y in part a are respectively , ________and _________.
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