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  3. Statistical Simulation in Python

Exercise

Fitness goals

Let's model how activity levels impact weight loss using modern fitness trackers. On days when you go to the gym, you average around 15k steps, and around 5k steps otherwise. You go to the gym 40% of the time. Let's model the step counts in a day as a Poisson random variable with a mean \(\lambda\) dependent on whether or not you go to the gym.

For simplicity, let’s say you have an 80% chance of losing 1lb and a 20% chance of gaining 1lb when you get more than 10k steps. The probabilities are reversed when you get less than 8k steps. Otherwise, there's an even chance of gaining or losing 1lb. Given all this information, find the probability of losing weight in a month.

Instructions

100 XP
  • Simulate steps as a Poisson random variable for a given day based on the value of lam.
  • Set prob to [0.2, 0.8] if steps > 10000 or to [0.8, 0.2] if steps < 8000. Sum up all the weight lost or gained in a month stored in w.
  • Calculate and print the fraction of simulations where total weight for a month in outcomes is less than 0. Save as weight_loss_outcomes_frac and use that to print your results.