Add forward-backward markdown.

Author: ctjoreilly

README.md

@@ -59,6 +59,7 @@ The file [aima3e-algorithms.pdf](https://github.com/aimacode/pseudocode/blob/mas
 | • |  | [LIKELIHOOD-WEIGHTING](md/Likelihood-Weighting.md) |
 | • |  | [GIBBS-ASK](md/Gibbs-Ask.md) |
 |<hr/>|<hr/>|<hr/>|
+| &bull; |  | [FORWARD-BACKWARD](md/Forward-Backward.md) |
 | &bull; |  |  |
 |<hr/>|<hr/>|<hr/>|
 | &bull; |  |  |

md/Forward-Backward.md

@@ -0,0 +1,20 @@
+# FORWARD-BACKWARD
+
+## AIMA3e
+__function__ FORWARD-BACKWARD(__ev__, _prior_) __returns__ a vector of probability distributions  
+ __inputs__: __ev__, a vector of evidence values for steps 1,…,_t_  
+&emsp;&emsp;&emsp;&emsp;&emsp;_prior_, the prior distribution on the initial state, __P__(__X__<sub>0</sub>)  
+&emsp;__local variables__: __fv__, a vector of forward messages for steps 0,&hellip;,_t_    
+&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;__b__, a representation of the backward message, initially all 1s  
+&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;__sv__, a vector of smoothed estimates for steps 1,&hellip;,_t_  
+
+&emsp;__fv__\[0\] &larr; _prior_  
+&emsp;__for__ _i_ = 1 __to__ _t_ __do__  
+&emsp;&emsp;&emsp;__fv__\[_i_\] &larr; FORWARD(__fv__\[_i_ &minus; 1\], __ev__\[_i_\])  
+&emsp;__for__ _i_ = _t_ __downto__ 1 __do__  
+&emsp;&emsp;&emsp;__sv__\[_i_\] &larr; NORMALIZE(__fv__\[_i_\] &times; __b__)  
+&emsp;&emsp;&emsp;__b__ &larr; BACKWARD(__b__, __ev__\[_i_\])  
+&emsp;__return__ __sv__
+
+---
+__Figure ??__ The forward\-backward algorithm for smoothing: computing posterior probabilities of a sequence of states given a sequence of observations. The FORWARD and BACKWARD operators are defined by Equations (__??__) and (__??__), respectively.