The triangle (call it <em>T </em>) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is
where <em>T</em> is the set
(a) I've attached an image of the integration region.
(b) <em>X</em> and <em>Y</em> are independent if the joint distribution is equal to the product of their marginal distributions.
Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:
Clearly, , so they are not independent.
Because they have the same denominator, add across
4 + 10 = 14
14/3 is your improper fraction answer.
To change it to a mixed fraction, find the whole number, and place the remainder over the denominator
14/3 = 4 2/3
4 2/3 is your mixed fraction answer
hope this helps
(5.3 x 10⁻²³ gram/molecule) x (20,000 molecule)
= (5.3 x 10⁻²³ x 2 x 10⁴) gram
= (10.6 x 10⁻²³⁺⁴) gram
= (1.06 x 10⁻²³⁺⁵) gram
= 1.06 x 10⁻¹⁸ gram