You are constructing a tangent line from a point outside a given circle to the circle. You have drawn the circle, a point outsid
2 answers:
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Answer:
The answer is of the population.
Step-by-step explanation:
The question is wrong. The joint density function is in R
and outside R.
R is defined as the rectangle ,
In order to find the fraction of the population satisfying the constraint , we will need to integrate the joint density function
over the region defined by the constraint. It is very convenient to draw the region ''R'' and the new region define by the constraint
I will attach a drawing with the region ''R'' and the new region where we need to apply the integral.
If we integrate outside ''R'', given that outside ''R'', the integral will be equal to 0 (because of the joint density function).
Inside the rectangle ''R'' and given the constraint , we define two new regions : the green region (I) and the blue region (II).
The final step is to integrate in (I) and in (II) and sum ⇒
⇒
, where ''1'' is the green region and ''2'' is the blue region.
⇒ +
=
We find that of the population satisfy the constraint
.
Answer:
We are given that:
Now we are asked to show that:
We know that:
Hence using equation (1) we get:
Also we know that:
and
so using above two formula in equation (2) we get:
( since we know that:
)
Hence we have proved that: