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LearnEdexcelYMA012018 specificationWST02 · Statistics 2Continuous distributions

WST02 · Module

Continuous distributions

2 subtopics≈ 70 min in total

Start the module: The continuous uniform distribution Open graphing calculator

The continuous uniform distribution
If $X$ is equally likely to be anywhere between $a$ and $b$ , then $X\sim U[a,b]$ . Its pdf is a flat rectangle of height $\dfrac1{b-a}$ , so any probability is just (width of the interval) ÷ (total width). Its mean is the midpoint and its variance is $\dfrac{(b-a)^2}{12}$ .
≈ 30 min
Normal approximations to the binomial and Poisson
For large $n$ with $p$ near $0.5$ , $B(n,p)$ is close to $N(np,\,np(1-p))$ . For large $\lambda$ , $\text{Po}(\lambda)$ is close to $N(\lambda,\lambda)$ . Because you're replacing whole numbers with a continuous curve, widen each value to an interval of half a unit either side: the continuity correction.
≈ 40 min