The video estimates the probability by counting how many simulated totals exceed 9 hours and dividing that count by the total number of trials. This implements the empirical-frequency estimator for the exceedance probability.
Conditions: The event is well-defined for each trial.; The denominator is the total number of simulated trials.
The video estimates the probability by counting how many simulated totals exceed 9 hours and dividing that count by the total number of trials. This implements the empirical-frequency estimator for the exceedance probability.
Conditions: The event is well-defined for each trial.; The denominator is the total number of simulated trials.
Setting `density=True` in `plt.hist` normalizes the bar heights so that the plotted histogram represents an empirical probability density estimate of the simulated total durations, rather than raw counts.
Conditions: Used when the goal is to compare the sample distribution with probability-density scale.; The plotted bars are normalized by bin width and sample size.
Setting `density=True` in `plt.hist` normalizes the bar heights so that the plotted histogram represents an empirical probability density estimate of the simulated total durations, rather than raw counts.
Conditions: Used when the goal is to compare the sample distribution with probability-density scale.; The plotted bars are normalized by bin width and sample size.
The two report completion-time arrays are generated using the `np.random.uniform` function. Report A is modeled by drawing `sims` independent values from a uniform distribution on the interval from 1 to 5 hours, and Report B is modeled by drawing `sims` independent values from a uniform distribution on the interval from 2 to 6 hours.
Conditions: Use the uniform model introduced earlier.; `sims` must already be defined.
The two report completion-time arrays are generated using the `np.random.uniform` function. Report A is modeled by drawing `sims` independent values from a uniform distribution on the interval from 1 to 5 hours, and Report B is modeled by drawing `sims` independent values from a uniform distribution on the interval from 2 to 6 hours.
Conditions: Use the uniform model introduced earlier.; `sims` must already be defined.
A red vertical line is placed at 9 on the histogram to mark the 9-hour barbecue deadline threshold. This makes it easier to visually identify the region corresponding to the event where the total time to complete both reports exceeds the deadline.
Conditions: The barbecue is in 9 hours.; The line marks the threshold on the horizontal axis.
A red vertical line is placed at 9 on the histogram to mark the 9-hour barbecue deadline threshold. This makes it easier to visually identify the region corresponding to the event where the total time to complete both reports exceeds the deadline.
Conditions: The barbecue is in 9 hours.; The line marks the threshold on the horizontal axis.
The video computes the total time to complete both reports by performing an elementwise addition of the two simulated completion-time arrays. The total time is simply their summation, represented in code as `duration = A+B`.
Conditions: A and B must be arrays of the same length.; Addition is performed entrywise across matched simulation runs.
The video computes the total time to complete both reports by performing an elementwise addition of the two simulated completion-time arrays. The total time is simply their summation, represented in code as `duration = A+B`.
Conditions: A and B must be arrays of the same length.; Addition is performed entrywise across matched simulation runs.