Louis = x
Jane = 2x (Twice as many as Louis)
Together they have 360
x + 2x = 360
3x= 360
x=120
2(120)= 240
Jane addresses 240 envelopes
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.)
A. 4x b. 3y c. 8p is the answer
Answer:
x=49750
Step-by-step explanation:
0.1(x + 250) = 5,000
Divide each side by .1
0.1(x + 250)/.1 = 5,000/.1
x+250 =50000
Subtract 250 from each side
x+250-250 = 50000-250
x=49750
Answer:
x + y ≤
3x + 5y ≥ 1100
Step-by-step explanation:
Given:
Seating capacity of theater = 250
Cost of each child ticket = $3
Cost of each adult ticket = $5
Cost per performance = $1100 at least
Find:
System of inequalities
Computation:
Let;
x = Number of children's tickets
y = Number of adult tickets
So
x + y ≤
3x + 5y ≥ 1100