Please explain clearly. Thank you!

There are n planets in a star system. On each planet, there is an astronomer who observes one of the other n 1 planets. All astronomers pick their planets to observe independently and uniformly at random. Let X be the number of planets that nobody is observing.

d) Find the variance Var(X), as a function of n. To simplify calculations, use approximations from parts (b) and (d) instead of the actual values. (Hint: Use part (d) to compute E(XiXj) for i = j, where Xi and Xj are indicator random variables you defined in part (b). You should get Var(X) [n(e-1)]/e2

From part b) upper bound on the probability that X n/2 is 2/e

(e) Apply Chebyshev's inequality to get an upper bound on the probability that X n/2. Use approximations E(X) n/e and Var(X) [n(e-1)]/e2 instead of the actual values.