Question

A joint density function of the continuous random variables x and y is a function f(x,...

A joint density function of the continuous random variables x and y is a function f(x, y) satisfying the following properties.

  1. f(x, y) ≥ 0 for all (x, y)

  2. ∞
    −∞
    ∞ f(x, y) dA = 1
    −∞
  3. P[(x, y)  R] =
      
    R
    f(x, y) dA

Show that the function is a joint density function and find the required probability.

f(x, y) =
1
8
,  		 0 ≤ x ≤ 1, 1 ≤ y ≤ 9
0,   elsewhere

P(0 ≤ x ≤ 1, 1 ≤ y ≤ 7)

Math   Statistics-And-Probability   
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