Find P(X > x) and show that P(X < 3) = 1-q*. Explain why P[X is odd(= 1,3,5,7, ..)]) = q x P[X is even(= 0,2,4,6, .-.)] And hence otherwise show that P(X is odd) = ; 1+9 Find P(X is odd|X < 3) as a function of q, and, given that

Suppose that f has a domain of [5, 13] and a range of [6, 16]. (a) What are the domain and range of the function y = f(x) + 2? (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*, *). Use the symbol ∞ for infinity and the appropriate type of parenthesis "(", ")", "[", or "]" depending on whether the interval is open or closed.) D= R =

Let f(n) and g(n) be functions satisfying  f(n) = {sqrt (n), 1 + f(n+1)} if sqrt (n) is an integer otherwise and g(n) = {sqrt (n), 2 + g(n+2)} if sqrt (n) is an integer othersiwe for postiive integers n. Find the least positive integer n such that f(n)/g(n) = 4/7