AP Statistics Curriculum 2007 Prob Rules

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(Addition Rule)
(Addition Rule)
Line 13: Line 13:
In general, for any ''n'',
In general, for any ''n'',
:<math>P(\bigcup_{i=1}^n A_i) =\sum_{i=1}^n P(A_i)
:<math>P(\bigcup_{i=1}^n A_i) =\sum_{i=1}^n P(A_i)
-
-\sum_{i,j\,:\,i<j}P(A_i\cap A_j) +\sum_{i,j,k\,:\,i<j<k}P(A_i\cap A_j\cap A_k)+ \cdots\cdots\ (-1)^{j+1} P(\bigcap_{i=1}^j A_i)+ \cdots\cdots\  +(-1)^{n+1} P(\bigcap_{i=1}^n A_i).</math>
+
-\sum_{i,j\,:\,i<j}P(A_i\cap A_j) +\sum_{i,j,k\,:\,i<j<k}P(A_i\cap A_j\cap A_k)+ \cdots\cdots\ +(-1)^{j+1} P(\bigcap_{i=1}^j A_i)+ \cdots\cdots\  +(-1)^{n+1} P(\bigcap_{i=1}^n A_i).</math>
=== Multiplication Rule===
=== Multiplication Rule===

Revision as of 03:57, 29 January 2008

Contents

General Advance-Placement (AP) Statistics Curriculum - Probability Theory Rules

Addition Rule

The probability of a union, also called the Inclusion-Exclusion principle allows us to compute probabilities of composite events represented as unions (i.e., sums) of simpler events.

For events A1, ..., An in a probability space (S,P), the probability of the union for n=2 is

P(A_1\cup A_2)=P(A_1)+P(A_2)-P(A_1\cap A_2),

For n=3,

P(A_1\cup A_2\cup A_3)=P(A_1)+P(A_2)+P(A_3) -P(A_1\cap A_2)-P(A_1\cap A_3)-P(A_2\cap A_3)+P(A_1\cap A_2\cap A_3)

In general, for any n,

P(\bigcup_{i=1}^n A_i) =\sum_{i=1}^n P(A_i)
-\sum_{i,j\,:\,i<j}P(A_i\cap A_j) +\sum_{i,j,k\,:\,i<j<k}P(A_i\cap A_j\cap A_k)+ \cdots\cdots\ +(-1)^{j+1} P(\bigcap_{i=1}^j A_i)+ \cdots\cdots\  +(-1)^{n+1} P(\bigcap_{i=1}^n A_i).

Multiplication Rule

Model Validation

Checking/affirming underlying assumptions.

  • TBD

Computational Resources: Internet-based SOCR Tools

  • TBD

Examples

Computer simulations and real observed data.

  • TBD

Hands-on activities

Step-by-step practice problems.

  • TBD

References

  • TBD



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