Question

Let X and Y be two jointly continuous random variables with joint PDF $f_{XY}(x, y) = egin{cases} e^{-xy} & 1 le x le e, y > 0\ 0 & ext{otherwise} end{cases}$ a. Find the marginal PDFs, $f_X(x)$ and $f_Y(y)$. b. Write an integral to compute $P(0 le Y le 1, 1 le X le sqrt{e})$.

          Let X and Y be two jointly continuous random variables with joint PDF
$f_{XY}(x, y) =  egin{cases} e^{-xy} & 1 le x le e, y > 0\ 0 & 	ext{otherwise} end{cases}$
a. Find the marginal PDFs, $f_X(x)$ and $f_Y(y)$.
b. Write an integral to compute $P(0 le Y le 1, 1 le X le sqrt{e})$.

Let X and Y be two jointly continuous random variables with joint PDF
fXY(x, y) = egincases e^-xy 1 le x le e, y > 0 0 extotherwise endcases
a. Find the marginal PDFs, fX(x) and fY(y).
b. Write an integral to compute P(0 le Y le 1, 1 le X le sqrte).

Added by Janet P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Rahi P

02/07/2022

Step 1

So, we have: \[f_X(x) = \int_{0}^{\infty} e^{-xy} dy\] \[= \left[-\frac{1}{x}e^{-xy}\right]_{0}^{\infty}\] \[= -\frac{1}{x}(0 - 1)\] \[= \frac{1}{x}\] Therefore, the marginal PDF of X is $f_X(x) = \frac{1}{x}$ for $1 < x < e$. ** Show more…

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Let X and Y be two jointly continuous random variables with joint PDF 1 < x < e, y > 0 e^(-xy) f(x,y) = otherwise a) Find the marginal PDFs, f(x) and f(y). b) Write an integral to compute P(0 < Y < 1, 1 < X < "∑"e).