Subjects algebra

Excel Formula 632E60

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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: $$\text{Result} = \begin{cases} 0 & \text{if } J3=0 \\ \frac{A14}{B14 \sqrt{4 \pi C14 J3}} \exp\left(-\frac{(D14 - F14 J3)^2}{4 C14 J3}\right) & \text{if } J3 \neq 0 \end{cases}$$