- A fair six-sided black die has faces numbered \(1,2,2,3,3\) and 4
The random variable \(B\) represents the score when the black die is rolled.
- Write down the value of \(\mathrm { E } ( B )\)
A white die has 6 faces numbered \(1,1,2,4,5\) and \(c\) where \(c > 5\)
The discrete random variable \(W\) represents the score when the white die is rolled and has probability distribution given by
| \(w\) | 1 | 2 | 4 | 5 | \(c\) |
| \(\mathrm { P } ( W = w )\) | \(a + b\) | \(a\) | 0.3 | \(a\) | \(b\) |
Greg throws the black die and Nilaya throws the white die. Greg wins the game if he scores at least two more than Nilaya, otherwise Greg loses.
The probability of Greg winning the game is \(\frac { 1 } { 6 }\) - Find the value of \(a\) and the value of \(b\)
Show your working clearly.
The random variable \(X = 2 W - 5\)
Given that \(\mathrm { E } ( X ) = 2.6\) - find the exact value of \(\operatorname { Var } ( X )\)
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