Question

1. A student asks her teacher "What is the probability that it will take you exactly 20 minutes to walk to school in the morning?" What will be the teacher's reply? What is a better question to ask? Explain by referring to concepts that we discussed in this unit. 2. Describe how calculating probability for continuous random variables is different than calculating probability for discrete random variables. Explain using examples discussed in the activity and ideas discussed in this unit.

Answer 1

1) The teacher's reply will be zero. This is because the space for the times it can take to reach school in the morning is

(0, oo)

Since this is an infinite space, the probability of any one number being chosen is zero (Assuming uniform distribution)

A better question to ask is the CDF function, specifically what is the probability that one will take less than 20 minutes to reach school in the morning

2) Probability for discrete variables is relative easier. The space for events is finite and the space for the event is smaller than this universal set. Taking a ratio of these two sets' sizes we get the probability of the event. For the continuous variable, we find the probability by finding a function such that
P(X =x)=f(x
which must satisfy some properties (like
f (x) dr 1
etc)