4. A spinner can land on the numbers \(10,12,14\) and 16 only and the probability of the spinner landing on each number is the same.
The random variable \(X\) represents the number that the spinner lands on when it is spun once.

1. State the name of the probability distribution of \(X\).
2. 1. Write down the value of \(\mathrm { E } ( X )\)
   2. Find \(\operatorname { Var } ( X )\) A second spinner can land on the numbers 1, 2, 3, 4 and 5 only. The random variable \(Y\) represents the number that this spinner lands on when it is spun once. The probability distribution of \(Y\) is given in the table below

      \(y\)	1	2	3	4	5
      \(\mathrm { P } ( Y = y )\)	\(\frac { 4 } { 30 }\)	\(\frac { 9 } { 30 }\)	\(\frac { 6 } { 30 }\)	\(\frac { 5 } { 30 }\)	\(\frac { 6 } { 30 }\)

3. Find
   1. \(\mathrm { E } ( Y )\)
   2. \(\operatorname { Var } ( Y )\) The random variable \(W = a X + b\), where \(a\) and \(b\) are constants and \(a > 0\) Given that \(\mathrm { E } ( W ) = \mathrm { E } ( Y )\) and \(\operatorname { Var } ( W ) = \operatorname { Var } ( Y )\)
4. find the value of \(a\) and the value of \(b\). Each of the two spinners is spun once.
5. Find \(\mathrm { P } ( W = Y )\)