Basic E(X) and Var(X) calculation

Questions that ask directly for the mean and/or variance of a binomial distribution X ~ B(n,p), or simple linear transformations Y = aX + b, without requiring probability calculations.

5 questions · Moderate -0.9

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CAIE S2 2003 June Q1
4 marks Easy -1.3
1 A fair coin is tossed 5 times and the number of heads is recorded.
  1. The random variable \(X\) is the number of heads. State the mean and variance of \(X\).
  2. The number of heads is doubled and denoted by the random variable \(Y\). State the mean and variance of \(Y\).
Edexcel S2 2024 January Q6
9 marks Moderate -0.3
  1. A bag contains a large number of counters with an odd number or an even number written on each.
Odd and even numbered counters occur in the ratio \(4 : 1\) In a game a player takes a random sample of 4 counters from the bag.
The player scores
5 points for each counter taken that has an even number written on it
2 points for each counter taken that has an odd number written on it
The random variable \(X\) represents the total score, in points, from the 4 counters.
  1. Find the sampling distribution of \(X\) A random sample of \(n\) sets of 4 counters is taken. The random variable \(Y\) represents the number of these \(n\) sets that have a total score of exactly 14
  2. Calculate the minimum value of \(n\) such that \(\mathrm { P } ( Y \geqslant 1 ) > 0.95\)
Edexcel S2 2005 June Q1
7 marks Easy -1.2
  1. It is estimated that \(4 \%\) of people have green eyes. In a random sample of size \(n\), the expected number of people with green eyes is 5 .
    1. Calculate the value of \(n\).
    The expected number of people with green eyes in a second random sample is 3 .
  2. Find the standard deviation of the number of people with green eyes in this second sample. expected number of people with green eyes is 5 .
  3. Calculate the value of \(n\) - The expected number of people with green eyes in a second random sample is 3 .
  4. sample. C) T. " D
OCR MEI Further Statistics Minor 2019 June Q1
7 marks Easy -1.3
1 In a game at a charity fair, a spinner is spun 4 times.
On each spin the chance that the spinner lands on a score of 5 is 0.2 .
The random variable \(X\) represents the number of spins on which the spinner lands on a score of 5 .
  1. Find \(\mathrm { P } ( X = 3 )\).
  2. Find each of the following.
    • \(\mathrm { E } ( X )\)
    • \(\operatorname { Var } ( X )\)
    One game costs \(\pounds 1\) to play and, for each spin that lands on a score of 5 , the player receives 50 pence.
    1. Find the expected total amount of money gained by a player in one game.
    2. Find the standard deviation of the total amount of money gained by a player in one game.
Edexcel S2 Specimen Q3
7 marks Moderate -0.3
A manufacturer of chocolates produces 3 times as many soft centred chocolates as hard centred ones. Assuming that chocolates are randomly distributed within boxes of chocolates, find the probability that in a box containing 20 chocolates there are
  1. equal numbers of soft centred and hard centred chocolates, [3]
  2. fewer than 5 hard centred chocolates. [2]
A large box of chocolates contains 100 chocolates.
  1. Write down the expected number of hard centred chocolates in a large box. [2]