Question

Write down the probability function of a Normal variate which has mean 8 and variance 9

Answer 1

Given, mean  μ = 8 and

variance σ² = 9 ⇒ σ = \(\sqrt9\) = 3

Probability function is normal distribution whose variance σ² and mean μ is

P(x,σ,μ) = \(\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\big(\frac{\mathrm{x}-\mu}{\sigma}\big)^2}\) , x ∈ R

then probability function for given problem is

P(x,σ,μ) = \(\frac{1}{3\sqrt{2\pi}}e^{-\frac{1}{2}\big(\frac{\mathrm{x}-8}{3}\big)^2}\)

= \(\frac{1}{3\sqrt{2\pi}}e^{-\frac{1}{18}(\mathrm{x}-8)^2}\) , x ∈ R