Edexcel A-Level Mathematics A2 S2.2.3 Relationship Between Density and Df X F X Questions

Practise relating probability densities to distribution functions with verified Edexcel IAL questions and mark-scheme evidence.

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The continuous random variable X has cumulative distribution function given by

\mathrm{F}(x)=\left\{\begin{array}{lr} 0 & x<-k \\ \frac{x+k}{4 k} & -k \leqslant x \leqslant 3 k \\ 1 & x>3 k \end{array}\right.

where k is a positive constant.

Specify fully, in terms of k, the probability density function of X

f(x)=\begin{cases}\dfrac{1}{4k}, & -k\leqslant x\leqslant 3k,\\ 0, & \text{otherwise.}\end{cases}

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