Step-by-step explanation:
Here is your answer
http://www.lasesp.com/article/16336607434947849/Surprise_Gift
From what I gather from your latest comments, the PDF is given to be
and in particular, <em>f(x, y)</em> = <em>cxy</em> over the unit square [0, 1]², meaning for 0 ≤ <em>x</em> ≤ 1 and 0 ≤ <em>y</em> ≤ 1. (As opposed to the unbounded domain, <em>x</em> ≤ 0 *and* <em>y</em> ≤ 1.)
(a) Find <em>c</em> such that <em>f</em> is a proper density function. This would require
(b) Get the marginal density of <em>X</em> by integrating the joint density with respect to <em>y</em> :
(c) Get the marginal density of <em>Y</em> by integrating with respect to <em>x</em> instead:
(d) The conditional distribution of <em>X</em> given <em>Y</em> can obtained by dividing the joint density by the marginal density of <em>Y</em> (which follows directly from the definition of conditional probability):
(e) From the definition of expectation:
(f) Note that the density of <em>X</em> | <em>Y</em> in part (d) identical to the marginal density of <em>X</em> found in (b), so yes, <em>X</em> and <em>Y</em> are indeed independent.
The result in (e) agrees with this conclusion, since E[<em>XY</em>] = E[<em>X</em>] E[<em>Y</em>] (but keep in mind that this is a property of independent random variables; equality alone does not imply independence.)
Answer: 12) 34° 13) 90°
<u>Step-by-step explanation:</u>
12) Given: a = 10.2, b = 6.8, A = 122°
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Law of Cosines: a² = b² + c² - 2bc · cos A
<em>Note: The letters can be swapped</em>
13) Given: a = 3, b = 4, c = 5, C = ???
3² = 4² + 5² - 2(4)(5) · cos C
9 = 16 + 25 - 40 cos C
9 = 41 - 40 cos C
-32 = -40 cos C
0.8 = cos C
90° = C
Answer:Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.
Step-by-step explanation: if you have 14 more than a number, you would have 14 + that number, would equal 56
Answer:
The answer should be m < -2.5
Step-by-step explanation:
I was taught this before and my teacher always said if its a open circle then its > or < if its a closed circle then it should have the line under it, and the line is going down so it would be Less than sign