2.1 List of probability distributions

2.1.1 Discrete distributions

Probability Mass Functions (PMF)

1. \(P(x) = \frac{1}{14} (a+2x); x = -3, -2, -1, 0, 1, 2, 3\)
2. \(P(x) = k(x-2); x = 3, 4,5,6,7,8\)
3. \(P(x) = \frac{x-1}{k}; x=2,3,4,5\)
4. \(P(x) = \frac{3-|4-x|}{k}; x=2,3,4,5,6\)
5. \(p(x) = \frac{x+4}{30}; x=0,1,2,3,4\)
6. \(P(x) = \frac{2x+k}{56}; x = -3, -2, -1, 0, 1, 2, 3\)
7. \(P(x) = \frac{x+1}{k}; x= 1,2,3,4\)

2.1.2 Continuous

Probability Density Functions (PDF)

1. \(f(x) = 2x; 0 < x < 1\)
2. \(f(x) = \frac{1}{30} (3+2x); 2 < x < 5\)
3. \(f(x) = ax^2; 0 < x < 4\)
4. \(f(x) = kx^2 + kx + \frac 18; 0 < x < 8\)
5. \(f(x) = kx; 0 < x < 4\)
6. \(f(x) = 3x^2; 0 \le x \le 1\)
7. \(f(y) = k(3y+5); 1 < y < 5\)
8. \(f(z) = \frac29 (3z-z^2); 0 \le x \le 3\)

2.1.2.1 Joint PDF

1. \[f(x,y) = 8xy; 0 < x, y <1\]
2. \[f(x,y) = \frac 3 2 (x+y); 0 < x, y <1\]
3. \[f(x,y) = 4x(1-y); 0 < x, y <1\]
4. \[f(x,y) = 6xy^2); 0 < x, y <1\]