First, use the fact that the sum of all probabilities must equal 1:

\(a + b + 0.15 + 0.4 = 1\)

\(a + b = 0.45\)

Next, use the given expected value \(E(X) = 0.75\):

\(E(X) = (-3)a + (-1)b + 0 \times 0.15 + 4 \times 0.4 = 0.75\)

\(-3a - b + 1.6 = 0.75\)

Simplify to find another equation:

\(-3a - b = -0.85\)

Now solve the system of equations:

1. \(a + b = 0.45\)

2. \(-3a - b = -0.85\)

Add the two equations to eliminate \(b\):

\(a + b - 3a - b = 0.45 - 0.85\)

\(-2a = -0.4\)

\(a = 0.2\)

Substitute \(a = 0.2\) back into the first equation:

\(0.2 + b = 0.45\)

\(b = 0.25\)

Thus, \(a = 0.2\) and \(b = 0.25\).