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Step-by-step explanation:
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Answer:
Cov (X,Y) = 6
Step-by-step explanation:
hello,
Cov(X,Y) = E(XY) - E(X)E(Y)
we must first find E(XY), E(X), and E(Y).
since X is uniformly distributed on the interval (0,12), then E(X) = 6.
next we find the joint density f(x,y) using the formula
this is because f is uniformly distributed on the the interval (0,12)
also since the conditional probability density of Y given X=x, is uniformly distributed on the interval [0,x], then
for 0≤y≤x≤12
thus
.
hence,
also,
thus Cov(X,Y) = E(XY) - E(X)E(Y)
= 24 - (6)(3)
= 6
Answer:
5 x 5 x 5 x 5 x 5
Step-by-step explanation:
109 divided by 9 is 12. So the answer is 9.
Maybe one of the easier ways to work this is to write the equation of the line through the points you know, then use that to find the point you don't know. The 2-point formula for a line is ...
... y = (y2 -y1)/(x2 -x1)·(x -x1) +y1
Filling in (x1, y1) = (3, 213) and (x2, y2) = (8, 568), you get ...
... y = (568 -213)/(8 -3)·(x -3) +213
... y = 71(x -3) +213 . . . . . . simplified a bit
Now, for x=5, the value of <em>a</em> is ...
... a = 71(5 -3) +213 = 142 +213 = 355
The value of <em>a</em> that results in a constant rate of change is 355.
_____
The equation can actually be simplified further to ...
... y = 71x