7. The random variable \(D\) is defined as
$$D = A - 3 B + 4 C$$
where \(A \sim \mathrm {~N} \left( 5,2 ^ { 2 } \right) , B \sim \mathrm {~N} \left( 7,3 ^ { 2 } \right)\) and \(C \sim \mathrm {~N} \left( 9,4 ^ { 2 } \right)\), and \(A , B\) and \(C\) are independent.
- Find \(\mathrm { P } ( \mathrm { D } < 44 )\).
The random variables \(B _ { 1 } , B _ { 2 }\) and \(B _ { 3 }\) are independent and each has the same distribution as \(B\). The random variable \(X\) is defined as
$$X = A - \sum _ { i = 1 } ^ { 3 } B _ { i } + 4 C .$$
- Find \(\mathrm { P } ( X > 0 )\).
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