[DATA] A Random Process: Trains Your daily commute to work requires that you cross railroad tracks. At this particular railroad crossing the trains tend to be long and slow. So, getting stopped by a train will likely make you late for work. You start recording data to determine the likelihood of arriving at the tracks while a train is there. Open data set 5_1_37 at www.pearsonhighered.com/sullivanstats, which contains the day number and whether a train was present, or not, for 200 consecutive days in which you drove to work. The column “Train” shows a series of 0s and 1s. In that column, a 0 indicates there was no train present and a 1 indicates that a train was present. The column “Aggregate Train” represents the cumulative number of times a train was present. The column “Aggregate Proportion Train” represents the cumulative proportion of times a train was present.
d. Were you stopped by a train on the 30th day?

Verified step by step guidance

1. Locate the data for the 30th day in the dataset, specifically focusing on the column labeled "Train."
2. Recall that in the "Train" column, a value of 1 indicates a train was present on that day, and a value of 0 indicates no train was present.
3. Check the value in the "Train" column for day 30 to determine if a train was present.
4. If the value is 1, it means you were stopped by a train on the 30th day; if it is 0, you were not stopped by a train on that day.
5. Use this information to answer the question about whether you were stopped by a train on the 30th day.

Key Concepts

Random Process

A random process is a sequence of random variables representing outcomes over time or space. In this context, the presence or absence of a train each day is a random event that can be modeled to analyze patterns or probabilities. Understanding this helps interpret the data as a time series of binary outcomes.

Binary Data and Indicator Variables

Binary data uses two possible values, often 0 and 1, to indicate the absence or presence of an event. Here, '0' means no train and '1' means a train was present. Indicator variables simplify analysis by converting categorical outcomes into numerical form for statistical calculations.

Cumulative Proportion

Cumulative proportion is the running total of occurrences of an event divided by the number of observations up to that point. It shows the proportion of days with trains present over time, helping to estimate the likelihood of encountering a train on any given day, such as the 30th day.