Question

11. The random variables X, Y have the following joint density function: $f(x,y) = egin{cases} K, & 0 le x le 2, 0 le y le 1, ext{and } 2y le x \ 0 & ext{elsewhere} end{cases}$ Sketch the region where $f$ is positive and answer the following questions: (a) Find the constant K (b) Find marginal densities of X and Y. (c) Find the conditional density of X, given Y = 0.8 (d) Find $P(X le 1.5, Y le 0.5)$ (e) Find $P(Y le 0.5 | X le 1.5)$

          11. The random variables X, Y have the following joint density function:
$f(x,y) = egin{cases} K, & 0 le x le 2,  0 le y le 1, 	ext{and } 2y le x \ 0 & 	ext{elsewhere} end{cases}$
Sketch the region where $f$ is positive and answer the following questions:
(a) Find the constant K
(b) Find marginal densities of X and Y.
(c) Find the conditional density of X, given Y = 0.8
(d) Find $P(X le 1.5, Y le 0.5)$
(e) Find $P(Y le 0.5 | X le 1.5)$

11. The random variables X, Y have the following joint density function:
f(x,y) = egincases K, 0 le x le 2, 0 le y le 1, extand 2y le x 0 extelsewhere endcases
Sketch the region where f is positive and answer the following questions:
(a) Find the constant K
(b) Find marginal densities of X and Y.
(c) Find the conditional density of X, given Y = 0.8
(d) Find P(X le 1.5, Y le 0.5)
(e) Find P(Y le 0.5 | X le 1.5)

Added by Harold M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ajiboye Tunde

Step 1

Sketch the region where f is positive: The region where f is positive is defined by the conditions $0 < x < 2$, $0 < y < 1$, and $2y < x$. This region is a triangle with vertices at $(0,0)$, $(2,1)$, and $(2,0)$. Show more…

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11. The random variables X, Y have the following joint density function: f(x,y) = { K, 0 ≤ x ≤ 2, 0 ≤ y ≤ 1, and 2y ≤ x 0 elsewhere Sketch the region where f is positive and answer the following questions: (a) Find the constant K (b) Find marginal densities of X and Y. (c) Find the conditional density of X, given Y = 0.8 (d) Find P(X ≤ 1.5, Y ≤ 0.5) (e) Find P(Y ≤ 0.5 | X ≤ 1.5)