Introduction to Statistics: Difference between revisions

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== Random Variables ==

It's usually possible to represent the outcome of experiments in terms of ~~a representation involving~~ integers or real numbers. For instance, in the case of flipping a coin, it becomes a little cumbersome to record the outcomes of multiple experiments. Let's say we ~~flip a coin four times~~, ~~and repeat this experiment twice~~. We might ~~have gotten the following outcomes from the two experiments.~~<br>

It's usually possible to represent the outcome of experiments in terms of integers or real numbers. For instance, in the case of flipping a coin, it becomes a little cumbersome to record the outcomes of multiple experiments. Let's say we poll ten people for their voting preferences (Republican - R, or Democrat - D) in two different electorial districts. Our results might look like this:<br>

<math>\{RRRDRRDRRR\}</math> and <math>\{DDDDDRDDDD\}</math><br>

But if we're only ~~really~~ interested in the ~~number of times that the coin turns up heads~~ in ~~four flips,~~ we ~~can~~ assign an integer value of 0 ~~to Tails~~ and 1 ~~to Heads. Adding~~ the the ~~values~~ together ~~for each experiment gives us what we were after in the first place~~.

But we're probably only interested in the overall breakdown in voting preference for each district. If we assign an integer value to each outcome, say 0 for Democrat and 1 for Republican, we can obtain a concise summary of the voting preference district by district by adding the results together.

@@ Line 95: / Line 95: @@
 == Random Variables ==
-It's usually possible to represent the outcome of experiments in terms of a representation involving integers or real numbers.  For instance, in the case of flipping a coin, it becomes a little cumbersome to record the outcomes of multiple experiments.  Let's say we flip a coin four times, and repeat this experiment twice.  We might have gotten the following outcomes from the two experiments.<br>
+It's usually possible to represent the outcome of experiments in terms of integers or real numbers.  For instance, in the case of flipping a coin, it becomes a little cumbersome to record the outcomes of multiple experiments.  Let's say we poll ten people for their voting preferences (Republican - R, or Democrat - D) in two different electorial districts.  Our results might look like this:<br>
-<math>\{HHTH\}</math> and <math>\{TTHH\}</math><br>
+<math>\{RRRDRRDRRR\}</math> and <math>\{DDDDDRDDDD\}</math><br>
-But if we're only really interested in the number of times that the coin turns up heads in four flips, we can assign an integer value of 0 to Tails and 1 to Heads.  Adding the the values together for each experiment gives us what we were after in the first place.
+But we're probably only interested in the overall breakdown in voting preference for each district.  If we assign an integer value to each outcome, say 0 for Democrat and 1 for Republican, we can obtain a concise summary of the voting preference district by district by adding the results together.

Introduction to Statistics: Difference between revisions

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