Question

Let X and Y be two random variables with the joint probability density function \(f_{X,Y}(x,y) = \begin{cases} 6xy & \text{if } 0 < y \le \sqrt{x} \le 1\\ 0 & \text{otherwise} \end{cases}\) Then, the conditional probability \(P(Y \ge \frac{1}{3} | X = \frac{2}{3})\) is

          Let X and Y be two random variables with the joint probability density function
\(f_{X,Y}(x,y) = \begin{cases} 6xy & \text{if } 0 < y \le \sqrt{x} \le 1\\ 0 & \text{otherwise} \end{cases}\)
Then, the conditional probability \(P(Y \ge \frac{1}{3} | X = \frac{2}{3})\) is

Let X and Y be two random variables with the joint probability density function
fX,Y(x,y) = 6xy if 0 < y ≤√(x)≤ 1
0 otherwise
Then, the conditional probability P(Y ≥(1)/(3) | X = (2)/(3)) is

Added by Brian F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ameer Said

03/03/2022

Step 1

This can be found by integrating the joint probability density function over the range of X. \[ f_Y(y) = \int_{0}^{1} 6xy \, dx = 3y \] Show more…

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