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I am working on an assignment and struggling to figure it out

Consider a RV $X \sim \text{Uniform}(3,8)$

  1. What is $P(-2 \leq X \leq 4)$?
  2. What is $P(a \leq X \leq b)$ where both $a$ and $b$ are in $[3, 8]$?

In the syllabus that has been given to us, I can't find anything about question 1. For question 2 I have said that $P([a, b]) = F(b) - F(a)$ for every subinterval $[a, b]$, and so it's equal to $$\frac{b - a}{8 - 3}$$

If anyone could give me a hint, or recommend a book to read since our syllabus is terrible it would be very much appreciated.

1 Answers 1

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  1. $\Pr(-2 \leq X \leq 4) = \Pr(-2 \leq X < 3) + \Pr(3 \leq X \leq 4) = \Pr(3 \leq X \leq 4)$.

  2. It's right.

For more on Uniform distribution: https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)

For more on "basic" probability: https://books.google.co.in/books/about/Probability_Random_Variables_And_Random.html?id=ZE9KZZA3eHQC