Choose two numbers X and Y independently at random from the unit interval [0, 1] with the uniform density. The probability that X² + y² > 0.16

Pick two numbers X and Y independently at random (with uniform density) in the interval [0, 1]. Find the probability that given that 0.04323 ⠀ X< Y < 53 100 31 100 X.

Choose a number B at random from the interval [0, 1] with uniform density. Find the probability that (a) 1/3 < B < 2/3(b) |B − 1/2| ≤ 1/4(c) B < 1/4 or 1 − B < 1/4(d) 3B2 < B

3. Let random variables X and Y be independent with joint density fe(x, y). Let Ix (0) and Iy (0) be the Fisher information of X and Y, respectively. Prove that the Fisher information I(x,y)(0) = Ix(0) + Iy(0).