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Possibility table and probability distribution function of a derived variable

Possibility table and probability distribution function of a derived variable

IB Year 6 | Grade 12

An unbiased die is in the form of a regular tetrahedron and has its faces numbered \(1\), \(2\), \(3\), \(4\) and when the die is thrown onto a horizontal table, the number of the face in contact with the table is noted. Two such dice are thrown and the score \(X\) is found by multiplying these numbers together.

  1. Obtain the probability distribution of \(X\)
  2. Derive the values of
    1. \(P(X > 8)\);
    2. \(E(X)\);
    3. \(Var(X)\).

Solution:

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Answer:(i) \(\mathrm{P}(X=x)=\frac1{16}\) for \(x=1,9,16\), \(\frac18\) for \(x=2,3,6,8,12\), and \(\frac3{16}\) for \(x=4\); zero otherwise. (ii)(a) \(\frac14\) (b) \(\frac{25}{4}\) (c) \(\frac{275}{16}\).

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