Let Fnnge1 be a sequence of cumulative distribution functions given by Fn(x) = begincases 0 & if x < -n x+n/2n & if -n le x < n 1 & if x ge n. endcases Which one of the following statements is true?

(B) Fn(x) converges for all x in R, but the limiting function is not a cumulative distribution function

Q21Section ST (Statistics (Q11–Q65))21 of 65

Pointwise limit of spreading cdfs

Let $\{F_n\}_{n\ge1}$ be a sequence of cumulative distribution functions given by $F_n(x) = \begin{cases} 0 & \text{if } x < -n \ \frac{x+n}{2n} & \text{if } -n \le x < n \ 1 & \text{if } x \ge n. \end{cases}$ Which one of the following statements is true?

Pick an option to check your answer. In a mock test a wrong answer here costs 1/3 mark.

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