6. Determine whether each of the following is true or false (note: the statement is true...
True or False (a) If X ∩ Y = ∅ then the two events X and Y are independent? (b) If event X is independent of event Y, then X^c is independent of Y? (c) For a discrete random variable X, we have limx->∞ pX(x) = 0? (d) For a continuous random variable X, we have limx->∞ fX(x) = 0? (e) For a continuous random variable X, we have limx->0 fX(x) ≤ 1? (f) For two discrete random variables X...
Determine whether the statement is true or false. If false, explain why or give a counterexample that shows it is false. (2 pts each) b. If f(x,y) S g(x, y) for all (x, y) in , and both f and g are continuous over 2, then c. If f is continuous over 2 and 22, and if JJ, dA- jJa,dA, then f(x.y) dA- Jf(x.y) dA for any function fx,y). Determine whether the statement is true or false. If false, explain...
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. In most applications, continuous random variables represent counted data, while discrete random variables represent measured data. Choose the correct answer below. O A. False. In most applications, discrete random variables represent counted data, while continuous random variables represent measured data. OB. True
True or False With explanation please. 1- True or false: a. If A is an event of a sample space with P(A)-P(AS), then P(A)-0.5 b. Under certain conditions, it is possible that the sum of the probabilities of all the sample points in a sample space is less than one P(A or B)-P(A)+P(B) P(A and B) P(A).P(B) by its own probability and then adding all the products together; that is P deviation of σ. If x is converted to the...
True/False [1pt each]: Circle T for True or F for False. 1. TIF If the events A and B are disjoint with probabilities P(A) 0.2 and P(B) 0.3, then A and B are independent. 2. T / F If P(A) = 0.6, P(B) 0.4, and P(AIB) = 0.6, then the events A and B are independent. 3. T F The number of heads in 100 tosses of a coin is a discrete random variable. 4 TIF P(AUB) P(A |B) P(B)...
Problem 1: Determine whether the statement is true or false. If the statement is true, then prove it. Otherwise, provide a counterexample. (a) If a continuous function f:R +R is bounded, then f'(2) exists for all x. (b) Suppose f.g are two functions on an interval (a, b). If both f + g and f - g are differentiable on (a, b), then both f and g are differentiable on (a,b). Problem 2: Define functions f,g: RR by: x sin(-),...
8) (10 points) Determine if the following are true or false. If false, explain why or give an example to counter the false statement. a) Two events are disjoint if the occurrence of one does not affect the other. b) It is not possible to get a probability of exactly 0. c) Drawing without replacement is an example of dependent events. d) It is possible to have both a disjoint event and an independent event. e) The standard deviation of...
TRUE OR FALSE _______23. Events are independent when the occurrence of one event has no effect on the probability that another will occur. _______24.The P(x) is always 0 ≤ P(x) ≤ 1. _______25. The mean of the discrete probability distribution for a discrete random variable is called its expected value
#55, 59 In Exercises 55 and 56, determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. 55. If f is continuous at x = a, then f is differentiable at x = a. 56. If f is continuous at x = a and g is differentiable at x = a, then lim f(x)g(x) = f(a)g(a). X 57. Sketch the...
Detailed proof please. . 1. Determine whether the following statements are true or false. If one is true, provide a proof. If one is false, provide a counterexample (proving that it is in fact a counterexample). IF f is a positive continuous function on [1,00) and (f(x))2dx converges, THEN Sº f(x)dx converges. • IF f is a positive continuous function on [1,00) such that limx700 f(x) O and soon f(x)dx converges, THEN S ° (f (x))2dx converges. IF f is...