Conditional probability with uniform

Questions asking for P(A|B) where both events involve a uniform random variable.

3 questions

Edexcel S2 2012 January Q1
  1. The time in minutes that Elaine takes to checkout at her local supermarket follows a continuous uniform distribution defined over the interval [3,9].
Find
  1. Elaine's expected checkout time,
  2. the variance of the time taken to checkout at the supermarket,
  3. the probability that Elaine will take more than 7 minutes to checkout. Given that Elaine has already spent 4 minutes at the checkout,
  4. find the probability that she will take a total of less than 6 minutes to checkout.
Edexcel FS2 AS 2018 June Q2
  1. The continuous random variable X has probability density function
$$f ( x ) = \begin{cases} \frac { 1 } { 8 } & 1 \leqslant x \leqslant 9
0 & \text { otherwise } \end{cases}$$
  1. Write down the name given to this distribution. The continuous random variable \(Y = 5 - 2 X\)
  2. Find \(\mathrm { P } ( Y > 0 )\)
  3. Find \(\mathrm { E } ( Y )\)
  4. Find \(\mathrm { P } ( Y < 0 \mid X < 7.5 )\)
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Edexcel FS2 AS 2022 June Q5
  1. The random variable \(X\) has the continuous uniform distribution over the interval [0.5, 2.5]
Talia selects a number, \(T\), at random from the distribution of \(X\)
  1. Find \(\mathrm { P } ( T < 1 )\) Malik takes Talia's number, \(T\), and calculates his number, \(M\), where \(M = \frac { 1 } { T ^ { 2 } }\)
  2. Find the probability that both \(T\) and \(M\) are less than 2.25 Raja and Greta play a game many times.
    Each time they play they use a number, \(R\), randomly selected from the distribution of \(X\)
    Raja's score is \(R\)
    Greta's score is \(G\), where \(G = \frac { 2 } { R ^ { 2 } }\)
  3. Determine, giving a reason, who you would expect to have the higher total score.