2.5.8 The random variable X measures the concentration of ethanol in a chemical solution, and the random variable Y measures the acidity of the solution. They have a joint probability density function...

2.5.8 The random variable X measures the concentration of
ethanol in a chemical solution, and the random variable Y
measures the acidity of the solution. They have a joint
probability density function

f(x, y) = A(20 - x - 2y)

Extracted text: 2.5.8 The random variable X measures the concentration of ethanol in a chemical solution, and the random variable Y measures the acidity of the solution. They have a joint probability density function f(x, y) = A(20 – x – 2y) for 0 < 5="" and="" 0="">< y="">< 5,="" and="" f="" (x,="" y)="0" elsewhere.="" (a)="" what="" is="" the="" value="" of="" a?="" (b)="" what="" is="" p(1="">< x="">< 2,="" 2="">< y="">< 3)?="" (c)="" construct="" the="" marginal="" probability="" density="" functions="" fx(x)="" and="" fr(y).="" (d)="" are="" the="" ethanol="" concentration="" and="" the="" acidity="" independent?="" (e)="" what="" are="" the="" expectation="" and="" the="" variance="" of="" the="" ethanol="" concentration?="" (f)="" what="" are="" the="" expectation="" and="" the="" variance="" of="" the="" acidity?="" (g)="" if="" the="" ethanol="" concentration="" is="" 3,="" what="" is="" the="" conditional="" probability="" density="" function="" of="" the="">