Q3: Consider the following probability distributions : (A) Normal distribution (B)... - Engineering Mathematics & Statistics - ICAR AIEEA PG Agricultural Engineering & Technology 09 July 2023 (Shift 1) Paper | Agrigyan

Detailed Analysis of Probability Distributions Properties:

• Normal Distribution: Mean = $\mu$, Variance = $\sigma^2$ (independent parameters; generally $\mu \ne \sigma^2$).
• Binomial Distribution: Mean = $np$, Variance = $npq$ (since $q \lt 1$, Mean > Variance).
• Poisson Distribution: Defined by single parameter $\lambda$. Mean = $\lambda$ and Variance = $\lambda$. Hence, Mean = Variance holds strictly for Poisson distribution only.
• F-distribution: Mean = $d_2 / (d_2 - 2)$ for $d_2 \gt 2$, Variance is a complex function of degrees of freedom.
• Chi-square Distribution: Mean = $k$, Variance = $2k$ (Variance = $2 \times$ Mean).