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Normal Poisson 18E634

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Normal Poisson 18E634


1. The first question asks about the Normal Ordinate, which is the value of the normal distribution's probability density function (PDF) at the mean (usually 0 for standard normal). The formula for the normal PDF is: $$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$ At the mean $x=\mu$, the exponent becomes zero, so: $$f(\mu) = \frac{1}{\sigma \sqrt{2\pi}}$$ For the standard normal distribution where $\sigma=1$, this simplifies to: $$f(0) = \frac{1}{\sqrt{2\pi}}$$ Thus, the Normal Ordinate is $\frac{1}{\sqrt{2\pi}}$, which corresponds to option (B). 2. The second question asks for the mean and standard deviation of the Poisson distribution. The Poisson distribution with parameter $\lambda$ has: - Mean $= \lambda$ - Variance $= \lambda$ - Standard deviation $= \sqrt{\lambda}$ Therefore, the mean and standard deviation are $\lambda$ and $\sqrt{\lambda}$ respectively, which corresponds to option (C).