We have the following equations based on the given information:

1. The sum of probabilities: \(p + q + r + 0.4 = 1\)

2. The expected value: \(-3p + 2r + 4 \times 0.4 = 2.3\)

3. The variance: \((-3)^2p + 2^2r + 4^2 \times 0.4 - 2.3^2 = 3.01\)

From equation 1, we have:

\(p + q + r = 0.6\)

From equation 2, we simplify:

\(-3p + 2r = 0.7\)

From equation 3, we simplify:

\(9p + 4r = 1.9\)

Solving \(-3p + 2r = 0.7\) and \(9p + 4r = 1.9\) simultaneously:

Multiply the first equation by 2:

\(-6p + 4r = 1.4\)

Subtract from the second equation:

\(9p + 6p = 1.9 - 1.4\)

\(15p = 0.5\)

\(p = \frac{1}{30}\)

Substitute \(p\) back into \(-3p + 2r = 0.7\):

\(-3 \times \frac{1}{30} + 2r = 0.7\)

\(-0.1 + 2r = 0.7\)

\(2r = 0.8\)

\(r = \frac{2}{5}\)

Substitute \(p\) and \(r\) into \(p + q + r = 0.6\):

\(\frac{1}{30} + q + \frac{2}{5} = 0.6\)

\(q = 0.6 - 0.4 - 0.0333\)

\(q = \frac{1}{6}\)