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.)
i think it' =-8abc(a+b-c)
Least to greatest: -5.5, -5, 5/11, 4/5, 5, 5.33 repeating
Hello there!
Surface Area = 4pir^2
First, we need to find our radius, since we have our diameter all we need to do is divide it by 2. That means, 10 divided by 2 equals 5.
Our radius is 5.
Now, we can plug it into the formula.
4(3.14)(5^2)
4(3.14)(25)
4(78.5)
4(78.5) = 314
Now, convert into pi.
314 = 100pi or 100Π
Answer:
1/11 = 0.09
Step-by-step explanation:
problem best done with a tree diagram. let's focus on the blue branch for child 1. the probability of child 1 getting a blue marble is 4/12. now since he's choosing randomly and we assuming that after giving it away, there is 12-1=11 marbles left, the second child will have the probability 3/11 of getting a yellow marble. multiple those probabilities
4/12 × 3/11
1/3 × 3/11
3/33
1/11