Question

2) Let $f_{xy}(x,y)$ be a joint density for the ordered pair $(X,Y)$ in which X and Y are continuous random variables. \begin{equation} f_{xy}(x,y) = \frac{1}{3}(x+y) \end{equation} $0 \le x \le 1$ $0 \le y \le 2$ a) Find the probability that X is less than 0.5 and Y is greater than 1. b) Find the probability that X is greater 0.75. c) Find the marginal density function on X, denoted by $f_x(x)$ d) Calculate E[X]

          2) Let $f_{xy}(x,y)$ be a joint density for the ordered pair $(X,Y)$ in which X and Y are continuous
random variables.
\begin{equation*}
f_{xy}(x,y) = \frac{1}{3}(x+y)
\end{equation*}
$0 \le x \le 1$
$0 \le y \le 2$
a) Find the probability that X is less than 0.5 and Y is greater than 1.
b) Find the probability that X is greater 0.75.
c) Find the marginal density function on X, denoted by $f_x(x)$
d) Calculate E[X]

2) Let fxy(x,y) be a joint density for the ordered pair (X,Y) in which X and Y are continuous
random variables.

fxy(x,y) = (1)/(3)(x+y)

0 ≤ x ≤ 1
0 ≤ y ≤ 2
a) Find the probability that X is less than 0.5 and Y is greater than 1.
b) Find the probability that X is greater 0.75.
c) Find the marginal density function on X, denoted by fx(x)
d) Calculate E[X]

Added by Daniel E.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

07/05/2023

Step 1

5 and Y is greater than 1 is given by: $$P(X<0.5, Y>1)=\int_{0}^{0.5}\int_{1}^{2}f_{xy}(x,y)dydx$$ Show more…

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2) Let $f_{xy}(x,y)$ be a joint density for the ordered pair (X,Y) in which X and Y are **continuous** random variables. $$f_{xy}(x,y)=\frac{1}{3}(x+y)$$ $$0\leq x\leq 1$$ $$0\leq y\leq 2$$ a) Find the probability that X is less than 0.5 and Y is greater than 1. b) Find the probability that X is greater 0.75. c) Find the marginal density function on X, denoted by $f_x(x)$ d) Calculate E[X]