Difference between revisions of "Science:MATH105 Probability/Lesson 1 DRV/1.01 Discrete Random Variables"

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These concepts are introduced assuming no prior knowledge of probability, but they are discussed with an assumption of integration. That is, probability is introduced as an application of of integration.  
 
These concepts are introduced assuming no prior knowledge of probability, but they are discussed with an assumption of integration. That is, probability is introduced as an application of of integration.  
  
==Discrete Random Variables==
+
==Probability==
  
 
In any experiment, only one '''outcome''' occurs. If we flip a coin, the outcome will be either "heads" (H) or "tails" (T). If the coin is a "fair" coin, it is equally likely that the coin will land as tails or heads.  
 
In any experiment, only one '''outcome''' occurs. If we flip a coin, the outcome will be either "heads" (H) or "tails" (T). If the coin is a "fair" coin, it is equally likely that the coin will land as tails or heads.  
  
 +
We are often interested in quantifying the '''probability''' that a certain outcome occurs. Suppose we toss a fair coin many times, the coin will be H 50% of the time and T 50% of the time. And so we say that the probability that a tossed coin will be heads, if it is a fair coin, is 0.5.
  
We are often interested in quantifying the '''probability''' that a certain outcome occurs. Suppose we toss a fair coin tossed two times, and want to the probability that the coin will land as tails both times.
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If we toss a fair coin two times, there are four possible outcomes:
  
There are four possible outcomes:
+
* HH
 +
* HT
 +
* TH
 +
* TT
  
HH
+
Because the coin is fair, each outcome is equally likely to occur. So, we assign the probability of 0.25 to each of these outcomes.
HT
+
TH
+
TT
+
 
+
Because the coin is fair, each outcome is equally likely to occur.  
+
  
  

Revision as of 12:37, 15 January 2012

Goal: to define discrete probability with an example"

Discrete vs Continuous Random Variables

to go on the "About" page", or elsewhere

In MATH 105, we deal with

  • discrete random variables, and
  • continuous random variables.

You will notice that certain definitions and concepts between them will be related.

These concepts are introduced assuming no prior knowledge of probability, but they are discussed with an assumption of integration. That is, probability is introduced as an application of of integration.

Probability

In any experiment, only one outcome occurs. If we flip a coin, the outcome will be either "heads" (H) or "tails" (T). If the coin is a "fair" coin, it is equally likely that the coin will land as tails or heads.

We are often interested in quantifying the probability that a certain outcome occurs. Suppose we toss a fair coin many times, the coin will be H 50% of the time and T 50% of the time. And so we say that the probability that a tossed coin will be heads, if it is a fair coin, is 0.5.

If we toss a fair coin two times, there are four possible outcomes:

  • HH
  • HT
  • TH
  • TT

Because the coin is fair, each outcome is equally likely to occur. So, we assign the probability of 0.25 to each of these outcomes.