Excel Formula 632E60
1. The problem is to understand and simplify the given Excel formula:
=IF(J3=0,"",(A14/(B14*SQRT(4*PI()*C14*J3)))*EXP(-((D14-F14*J3)^2)/(4*C14*J3)))
2. This formula calculates a value based on several cell references and a condition. The IF function checks if $J3=0$. If true, it returns an empty string ""; otherwise, it computes the expression.
3. The expression is:
$$\frac{A14}{B14 \sqrt{4 \pi C14 J3}} \times \exp\left(-\frac{(D14 - F14 J3)^2}{4 C14 J3}\right)$$
4. This resembles a probability density function of a normal distribution with parameters involving $C14$ and $J3$, scaled by $A14/B14$.
5. Step-by-step:
- Compute the denominator inside the square root: $4 \pi C14 J3$
- Take the square root: $\sqrt{4 \pi C14 J3}$
- Divide $A14$ by $B14$ times this square root.
- Compute the exponent numerator: $(D14 - F14 J3)^2$
- Compute the exponent denominator: $4 C14 J3$
- Calculate the exponent: $-\frac{(D14 - F14 J3)^2}{4 C14 J3}$
- Calculate the exponential: $\exp(\text{exponent})$
- Multiply the fraction by the exponential.
6. The formula returns this value only if $J3 \neq 0$, otherwise it returns an empty string.
Final simplified expression:
$$\text{Result} = \begin{cases} 0 & \text{if } J3=0 \\ \frac{A14}{B14 \sqrt{4 \pi C14 J3}} \exp\left(-\frac{(D14 - F14 J3)^2}{4 C14 J3}\right) & \text{if } J3 \neq 0 \end{cases}$$