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Recall that the "floor" of a real number x , denoted ⌊x⌋ , is the largest integer ≤x $$F(x)= \left\{ \begin{array} \\ k-\frac{1}{\lfloor x\rfloor}, x\ge 1,\\ 0, x\lt 1,\end{array} \right.$$ is a cumulative distribution function (cdf) for some fixed number k . Find k.

Can someone help me in drawing the graph of this function? I don't know how to find the k. Someone please give me a hint to solve this problem; thank you.

J. W. Tanner
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ritul 26
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1 Answers1

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Your function is a stairstep, jumping at each natural greater than $0$. For $1 \le x \lt 2$ it is $k-1$, then for $2 \le x \le 3$ it is $k-\frac 12$ and so on.

For any cdf you need the limit as $x \to \infty$ to be $1$, as the probability that $x$ is less than $\infty$ is $1$.

Ross Millikan
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