exercise:68fed5f94a: Difference between revisions
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for a constant <math>c</math>. Determine the marginal density of <math>2Y^{1/2}</math> given <math>X=1/2</math>. | for a constant <math>c</math>. Determine the marginal density of <math>2Y^{1/2}</math> given <math>X=1/2</math>. | ||
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<li> | <li> | ||
<math display = "block"> | <math display = "block"> | ||
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\end{cases} | \end{cases} | ||
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Latest revision as of 02:40, 18 March 2024
The joint density function for the random variables [math]X,Y [/math] equals
[[math]]
f_{X,Y}(x,y) = \begin{cases}
cxy^3, y^2 \lt x \lt y, 0 \lt y \lt 1 \\
0, \, \textrm{Otherwise}
\end{cases}
[[/math]]
for a constant [math]c[/math]. Determine the marginal density of [math]2Y^{1/2}[/math] given [math]X=1/2[/math].
-
[[math]] g(z)= \begin{cases} \frac{z^7}{6}, \sqrt{2} \lt z \lt 2^{3/4} \\ 0, \, \textrm{Otherwise} \end{cases} [[/math]]
- [[math]] g(z)= \begin{cases} \frac{64z^3}{3}, \frac{1}{2} \lt z \lt \frac{1}{\sqrt{2}} \\ 0, \, \textrm{Otherwise} \end{cases} [[/math]]
- [[math]] g(z)= \begin{cases} z^3, \sqrt{2} \lt z \lt 2^{3/4} \\ 0, \, \textrm{Otherwise} \end{cases} [[/math]]
- [[math]] g(z)= \begin{cases} \frac{255z^7}{1688}, \frac{1}{2} \lt z \lt \frac{1}{\sqrt{2}} \\ 0, \, \textrm{Otherwise} \end{cases} [[/math]]
- [[math]] g(z)= \begin{cases} \frac{2^{7/2}z^{5/2}}{5}, 0 \lt z \lt 2 \\ 0, \, \textrm{Otherwise} \end{cases} [[/math]]