Convert 4.08 to a fraction. Help me please.
2 answers:
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<u>ANSWER:</u>
4 batches of cupcakes can be made.
<u>SOLUTION: </u>
Given, we need cups of flour for each batch of cupcakes. And we have 17 cups of flour.
We need to find how many batches can be made.
1st way:
We will get the number of batches when we divide the available cups with cups required for one batch.
Available cups = 17 and required cups for one batch = =
cups
number of batches =
= 4.857
As the number of batches can’t be fraction, we will neglect the fractional part.
2nd way:
Let the number of batches be x.
Then, cups of flour required for batches must be less than available flour
(x)() < 17
(x)(7) < (2)(17)
7x < 34
x <
x < 4.857
As the number of batches must be an whole number, x becomes 4.
Hence, 4 batches of cupcakes can be made.
(1) Looks like the joint density is
In order for this to be a proper density function, integrating it over its support should evaluate to 1. The support is a triangle with vertices at (0, 0), (4, 0), and (4, 4) (see attached shaded region), so the integral is
(2) The region in which <em>X</em> > 2 and <em>Y</em> < 1 corresponds to a 2x1 rectangle (see second attached shaded region), so the desired probability is
(3) Are you supposed to find the marginal density of <em>X</em>, or the conditional density of <em>X</em> given <em>Y</em>?
In the first case, you simply integrate the joint density with respect to <em>y</em>:
In the second case, we instead first find the marginal density of <em>Y</em>:
Then use the marginal density to compute the conditional density of <em>X</em> given <em>Y</em>:
