NormDist

### Program Information

Name: NormDist
Domain: Numerical Program
Functionality: Computing the Normal Distribution Probability value of a section
Input: The Mean Value  $\mu$ and the Variance $\sigma$.Figure 1 is the graph of Normal Distribution.  Take symbols a1, b1, c2, d2, e3 and f4 as 6 values that are belong to section 1, 1, 2, 2, 3 and 4 respectively.
Output: The Normal Distribution Probability value,expressed as NormDist().

#### Reference

Security Assurance with Program Path Analysis and Metamorphic Testing https://doi.org/10.1109/ICSESS.2013.6615286

### MR Information

#### MR1------

Description:
Property: $\rm NormDist(a1,c2) = NormDist(e3, f4)$ where $\rm e3=2\mu-c2, f4 =2\mu-a1$
Source input: $\rm (a1,c2)$
Source output: $\rm NormDist(a1,c2)$
Follow-up input: $\rm (e3,f4)$
Follow-up output: $\rm NormDist(e3, f4)$
Input relation: $(a1,c2) \Rightarrow (e3,f4)$ where $\rm e3=2\mu-c2, f4 =2\mu-a1$
Output relation: $\rm NormDist(a1,c2) = NormDist(e3, f4)$
Pattern:

#### MR2------

Description:
Property: $\rm NormDist(a1, e3) = NormDist(a1, c2) + NormDist(c2, d2) + NormDist(d2, e3)$ where $\rm e3=2\mu-c2, f4 =2\mu-a1$
Source input: $\rm (a1,c2)$
Source output: $\rm NormDist(a1,c2)$
Follow-up input: $\rm (a1,e3),(c2,d2),(d2,e3)$
Follow-up output: $\rm NormDist(a1, e3),NormDist(c2, d2),NormDist(d2, e3)$
Input relation: $(a1,c2) \Rightarrow (a1,e3),(c2,d2),(d2,e3)$ where $\rm e3=2\mu-c2, f4 =2\mu-a1$
Output relation: $\rm NormDist(a1, e3) = NormDist(a1, c2) + NormDist(c2, d2) + NormDist(d2, e3)$
Pattern:

#### MR3------

Description:
Property: $\rm NormDist(a1, f4) - NormDist(d2, e3) = 2 \times (NormDist(a1, b1)+NormDist(b1, c2)+NormDist(c2, d2)) = \\ 2\times (NormDist(d2, f4) - NormDist(d2, e3))$ where $f4=2\mu -a1, e3=2\mu -d2$
Source input:  $\rm (a1,d2)$
Source output:  $\rm NormDist(a1,d2)$
Follow-up input: $(a1,f4),(d2,e3),(a1,b1),(b1,c2),(c2,d2),(d2,f4),(d2,e3)$
Follow-up output:  $\rm NormDist(a1,f4),NormDist(d2,e3),NormDist(a1,b1),NormDist(b1,c2),NormDist(c2,d2),NormDist(d2,f4),NormDist(d2,e3)$
Input relation: $(a1,d2) \Rightarrow (a1,f4),(d2,e3),(a1,b1),(b1,c2),(c2,d2),(d2,f4),(d2,e3)$ where $f4=2\mu -a1, e3=2\mu -d2$
Output relation: $\rm NormDist(a1, f4) - NormDist(d2, e3) = 2 \times (NormDist(a1, b1)+NormDist(b1, c2)+NormDist(c2, d2)) = \\ 2\times (NormDist(d2, f4) - NormDist(d2, e3))$
Pattern:
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