• Mode of Snedecor's F-Distribution:
• For an $F$-distribution with $\nu_1$ numerator degrees of freedom and $\nu_2$ denominator degrees of freedom, the probability density function is unimodal for $\nu_1 \gt 2$.
• Differentiating the PDF with respect to $F$ and setting $\frac{df(F)}{dF} = 0$, the mode is found at:

• Key Moments of F-Distribution:
• Mean: $E(F) = \frac{\nu_2}{\nu_2 - 2}$ (for $\nu_2 \gt 2$)
• Variance: $\text{Var}(F) = \frac{2\nu_2^2(\nu_1 + \nu_2 - 2)}{\nu_1(\nu_2 - 2)^2(\nu_2 - 4)}$ (for $\nu_2 \gt 4$)
• Conclusion: The mode is given by $\frac{\nu_2(\nu_1 - 2)}{\nu_1(\nu_2 + 2)}$ (Option 1).

Correct option: (1) 1V2(V1-2)NV4(V2+2)]