16 The discrete random variable \(X\) has probability distribution
| \(\boldsymbol { x }\) | 1 | 2 | 3 | 4 | 5 | 6 |
| \(\mathbf { P } ( \boldsymbol { X } = \boldsymbol { x } )\) | 0.3 | 0.1 | 0.2 | 0.1 | 0.1 | 0.2 |
The discrete random variable \(Y\) has probability distribution
| \(\boldsymbol { y }\) | 2 | 3 | 4 | 5 | 6 | 7 |
| \(\mathbf { P } ( \boldsymbol { Y } = \boldsymbol { y } )\) | 0.3 | p | 0.2 | 0.1 | p | \(3 \mathrm { p } + 0.05\) |
It is claimed that \(\mathrm { P } ( X \geq 3 )\) is greater than \(\mathrm { P } ( Y \leq 4 )\)
Determine if this claim is correct.
Fully justify your answer.
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