The quantity of petrol, X (in thousands of liters), sold by a gas station daily is a continuous random variable with density function f (x) =

⎧⎪⎨⎪⎩

cx, 0 ≤ x < 2, 2c, 2 ≤ x < 4, c(6 − x), 4 ≤ x ≤ 6.

(i) Find the value of the constant c.

(ii) Calculate the probabilities P(X > 2), P(1 < X < 3), P(X ≤ 5|X > 1).

(iii) Find the expected value and the standard deviation for the quantity of petrol sold daily.