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).