50 couples are assigned to a round table randomly. Let X be the number of couples that sits together. Calculate the expectation and the variance of X.
50 couples are assigned to a round table randomly. Let X be the number of couples that sits together. Calculate the expectation and the variance of X.
6) At a restaurant, fifteen couples are seated at a large round table with thirty seats. Before the couples arrive, the waiter puts a card on each plate with the name of one person on it. Assume that the cards are placed randomly (with no attention to a person's gender or which person is a partner of which other person); that is, al rearrangements of the name cards are equally likely. What is the expected value of the number of...
6) At a restaurant, fifteen couples are seated at a large round table with thirty seats. Before the couples arrive, the waiter puts a card on each plate with the name of one person on it. Assume that the cards are placed randomly (with no attention to a person's gender or which person is a partner of which other person); that is, all rearrangements of the name cards are equally likely. What is the expected value of the number of...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events Ai = (ith couple sit next to each other2, 3. Count carefully the numbers of arrangements in...
O RANDOM VARIABLES AND DISTRIBUTIONS Expectation and variance of a random variable Let X be a random variable with the following probability distribution: Value x of X P(X-) 0.35 0.40 0.10 0.15 10 0 10 20 Find the expectation E (X) and variance Var(X) of X. (If necessary, consult a list of formulas.) Var(x) -
Let X be normally distributed random variable with expectation 5 and variance 16. Determine the values of c and d such that, Y := d + cX falls between [9, 11] with probability 0.95.
3, Let X be a Poisson random variable with parameter λ. Calculate the conditional expectation of X given that X is odd.
Let X be the number of pizzas sold and W be the number of burgers sold during a day at MeanGreen restaurant. X and W are random variables with E(X) 20 and E(W) 50 The prices of a pizza and a burger are $10 and S7, respectively. (a) (4 points) Find the expected daily revenue from pizza and burger sales (Hint: define R = 10X + 7W and use the expectation operator, E). (b) (4 points) Suppose Var(X) = 50,...
Question 9 Let X and Y be the number of hours that a randomly selected person watches movies and sporting events, respectively, during a three-month period. The following information is known about X and Y: E(X) = 50 E(Y) = 20 Var(X) = 50 Var(Y) = 30 Cov(X,Y) = 10 One hundred people are randomly selected and observed for these three months. Let T be the total number of hours that these one hundred people watch movies or sporting events...
Two balls are placed randomly into two boxes labeled as I and II. Let X denote the number of balls in box I and Y denote the number of occupied boxes. (a) Find the joint density function of X and Y. (b) Compute E(X) and the conditional expectation E(X|Y= 1).
(5) 2. Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose that the distribution of X is as follows: T 1 2 3 p(x) 3 .2 .5 A a random sample of size n-3 is selected. a) find pmf of Xn and construct a histogram, b) give two smallest values of S2, (S2 is the sample variance) and find their probabilities.
(5) 2. Let X be the number of...