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MissTica
3 years ago
5

Can you please help me with this question ​

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
5 0
Lol I don’t know the answer I jus need points but I think it’s math and the answer is B 1+2+7
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Let f(x) = cxe−x2 if x ≥ 0 and f(x) = 0 if x < 0.
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(a) If <em>f(x)</em> is to be a proper density function, then its integral over the given support must evaulate to 1:

\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx = \int_0^\infty cxe^{-x^2}\,\mathrm dx=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> → ∞:

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\displaystyle\int_1^3 2xe^{-x^2}\,\mathrm dx = \boxed{\frac{e^8-1}{e^9}} \approx 0.3678

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