(a) If <em>f(x)</em> is to be a proper density function, then its integral over the given support must evaulate to 1:
For the integral, substitute <em>u</em> = <em>x</em> ² and d<em>u</em> = 2<em>x</em> d<em>x</em>. Then as <em>x</em> → 0, <em>u</em> → 0; as <em>x</em> → ∞, <em>u</em> → ∞:
which reduces to
<em>c</em> / 2 (0 + 1) = 1 → <em>c</em> = 2
(b) Find the probability P(1 < <em>X </em>< 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):
Answer:
Step-by-step explanation:
This question asks you to compare the coordinates of the vertex of each function.
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The vertex of the function is its minimum, the point where the graph stops decreasing and starts increasing. It is the lowest point on the graph.
<h3>f(x)</h3>
The vertex is (-4, -1). The minimum is -1, located at x = -4.
<h3>g(x)</h3>
The vertex is (1, -25). The minimum is -25, located at x = 1. We know this is the minimum because there are no g(x) values that are lower (more negative).
<h3>comparison</h3>
The minimum of f(x), -1, is greater than the minimum of g(x), -25. TRUE
The x-value of f(x) at its minimum, -4, is less than the x-value of g(x) at its minimum, 1. TRUE
Answer:
Step-by-step explanation:
no, as 8 is not <2
Answer:
Decimal Form:
1.833333 (add a line over 3 because the answer is 1.83 repeated)
Mixed Number Form:
1 5/6
