Probability and Random Variables

Consider discrete random variables X and Y with probabilities as follows: P(X = 0 and Y = 0) = $\frac{1}{4}$ P(X = 1 and Y = 0) = $\frac{1}{8}$ P(X = 0 and Y = 1) = $\frac{1}{2}$ P(X = 1 and Y = 1) = $\frac{1}{8}$ Given...

Let X and Y be continuous random variables with probability density functions Px(x) and Py(y), respectively. Further, let Y = X^2 and Px(x) = {1, x ∈ (0,1] {0, otherwise Which one of the following options is correct?