(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:
y=-3x+6
Step-by-step explanation:
that equation gives the answer for all the 'y'
Answer:
Emily should use 160mL of oil
Step-by-step explanation:
If you only have 40mL of vinegar you would have to cut the recipe by 1.5
60/1.5=40
240/1.5=160
Answer:
Step-by-step explanation:
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that its curvature need not be zero.