Final answer:
To calculate P(Y>0.5 | X=0.8), we can use the conditional probability formula and integrate the joint probability density function f(x, y) to find the required probabilities.
Step-by-step explanation:
To calculate P(Y>0.5 | X=0.8), we need to use the conditional probability formula: P(Y>0.5 | X=0.8) = P(X=0.8 and Y>0.5) / P(X=0.8). In this case, we have the joint probability density function f(x, y). We can find P(X=0.8) by integrating f(x, y) with respect to y from 0.5 to 1, and then dividing the result by the integral of f(x, y) with respect to y from 0 to 1. Once we have P(X=0.8), we can then find P(X=0.8 and Y>0.5) by integrating f(x, y) with respect to y from 0.5 to 1. After finding both probabilities, we can divide P(X=0.8 and Y>0.5) by P(X=0.8) to get the final result.