Latest build deployed.

2026-01-22 10:53:53 -05:00
parent 8a2eeb03e7
commit 62c6585ee6
16 changed files with 80 additions and 17 deletions
@@ -313,7 +313,7 @@ var ptx_lunr_docs = [
  "type": "Section",
  "number": "",
  "title": "Tuesday, Jan 20",
-  "body": " Tuesday, Jan 20   This is an outline of the topics we covered in class. These notes are not a substitute for your own note-taking. I highly recommend that you take your own notes during class. If you ever miss a class for any reason, reach out to another student in class to get a copy of their notes.    Sec 2.1: Random Variables    A random variable is a function .    The idea is that is a variable representing a real number value which depends on the outcome of an experiment.    An experiment consists of planting 50 seeds in a garden, then growing them for 3 months. Let be the height of plant . Let be the number of seeds that didn't sprout. Let     A random variable has its own probability distribution.    Roll a fair D6 twice. Let be the sum of the rolls. Then has 36 elements. Since the die is fair, the distribution on is uniform, i.e., for any .   takes on the values , with probabilities:   Distribution for        2  1\/36    3  2\/36    4  3\/36        7  6\/36    8  5\/36        12  1\/36     Note that the distribution on is uniform, but the distribution on is not.      Let be a sample space and an event. Let  is called an indicator random variable , and we say \"  indicates  \".  The distribution on is:       Suppose we flip a coin times. Let indicate heads on flip . Let be the total number of heads in all flips. Then: If is the probability of the coin coming up heads on a flip, then has the binomial distribution with parameters . We'll use the notation and:   Suppose the coin has and we flip it times. Find .  The relevant flip sequences are: Each individual sequence has a probability of . So the total probability is: That is, (number of flip sequences)(probability of each sequence).     "
+  "body": " Tuesday, Jan 20   This is an outline of the topics we covered in class. These notes are not a substitute for your own note-taking. I highly recommend that you take your own notes during class. If you ever miss a class for any reason, reach out to another student in class to get a copy of their notes.    HW 1 Q5  Write for the event that there's a fire and for the event that there's visible smoke. Then the information we're given can be interpreted as: In this case, we can use the simpler version of Bayes' Theorem: Unlike our usual diagnostic testing examples, we do have access to the denominator probability here.    Sec 2.1: Random Variables    A random variable is a function .    The idea is that is a variable representing a real number value which depends on the outcome of an experiment.    An experiment consists of planting 50 seeds in a garden, then growing them for 3 months. Let be the height of plant . Let be the number of seeds that didn't sprout. Let     A random variable has its own probability distribution.    Roll a fair D6 twice. Let be the sum of the rolls. Then has 36 elements. Since the die is fair, the distribution on is uniform, i.e., for any .   takes on the values , with probabilities:   Distribution for        2  1\/36    3  2\/36    4  3\/36        7  6\/36    8  5\/36        12  1\/36     Note that the distribution on is uniform, but the distribution on is not.      Let be a sample space and an event. Let  is called an indicator random variable , and we say \"  indicates  \".  The distribution on is:       Suppose we flip a coin times. Let indicate heads on flip . Let be the total number of heads in all flips. Then: If is the probability of the coin coming up heads on a flip, then has the binomial distribution with parameters . We'll use the notation and:   Suppose the coin has and we flip it times. Find .  The relevant flip sequences are: Each individual sequence has a probability of . So the total probability is: That is, (number of flip sequences)(probability of each sequence).     "
 },
 {
  "id": "def-RV",