Lecture 4: Normal distribution

In today's lecture, we learnt two approximations.

1. Binomial distribution to normal distribution

If X~B(n, p)

• Recall that if when n is large, and np is smaller than 5, we can approximate X to Poisson distribution with mean np, i.e. X~Po(np)
• If n is large, np is larger than 5 and n(1-p) is also larger than 5, we can approximate X to Normal distribution with mean np and variance np(1-p), i.e. X~N(np, np(1-p)

2. Poisson distribution to normal distribution

If \[X \sim Po(\lambda)\], and \[\lambda>5\],

we can approximate X to normal distribution, \[X \sim N(\lambda,\lambda)\]

Remark: Remember to do the continuity correction when you approximate either Binomial or Poisson distribution to Normal distribution.

You can attempt tutorial 15B now.