Arithmetic sequence uniform distribution

A question is this type if and only if the discrete uniform distribution takes values in an arithmetic sequence like {a, a+k, a+2k, ...} rather than consecutive integers.

2 questions · Standard +0.0

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OCR MEI Further Statistics Minor 2022 June Q6
7 marks Standard +0.8
6 The random variable \(X\) has a uniform distribution over the values \(\{ 1,4,7 , \ldots , 3 n - 2 \}\), where \(n\) is a positive integer.
  1. Determine \(\operatorname { Var } ( X )\) in terms of \(n\).
  2. Given that \(n = 100\), find the probability that \(X\) is within one standard deviation of the mean.
Edexcel S1 Q1
6 marks Moderate -0.8
Thirty cards, marked with the even numbers from 2 to 60 inclusive, are shuffled and one card is withdrawn at random and then replaced. The random variable \(X\) takes the value of the number on the card each time the experiment is repeated.
  1. What must be assumed about the cards if the distribution of \(X\) is modelled by a discrete uniform distribution? [1 mark]
  2. Making this modelling assumption, find the expectation and the variance of \(X\). [5 marks]