Let X be the number of pizzas sold and W be the number of burgers sold...
Jon Snow consumes pizza and burgers. His utility function is u(P, B) = PB where P is the number of pizzas and B is the number of burgers. Jon Snow has $30 to spend, and he plans to spend it all on pizza and burgers. The price of one pizza is $10 and the price of one burger is $3. (a) Find and label Jon Snow’s initial optimal bundle on a graph where pizza is on the x-axis and burgers...
3. Bob is serving burgers at his restaurant. His children, Louise, Gene, and Tina, check a batch of 50 burger patties before the restaurant opens and find that 45 are safe to eat (5 have E. coli...oh, no!). Unfortunately, his children forgot to tell Bob which ones are unsafe to eat. Let X be the number of unsafe burgers in a randomly drawn sample of 10 burgers from the batch (a) Compute the probability that more than 1 burger drawn...
Ann, owner of Terrific Burgers in Weatherford, Texas decides to estimate the empirical demand function for her firm’s burgers. She collects data on the last 24 months of Burger sales from her own firm records. She knows the price she charged for her Burgers during that time period, and she also has kept a record of the prices charged by one of her close competitor, Stormy Burgers. Ann is able to obtain average household income figures from the Small Business...
Let X be the number of customers arriving in a given minute at the drive-up window of a local bank, and let Y be the number who make withdrawals. Assume that X is Poisson distributed with expected value E(X) = 3, and that the conditional expectation and variance of Y given X = x are E(Y|x) = x/2 and Var(Y |x)= (x + 1)/3. (a) Find E(Y) (b) Var(Y) (c) Find E(XY). 20.
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...
2) Pizza and Calzones, Revisited A pizza vendor sells pizzas and calzones at a sporting event. Since it is very well attended, the vendor is certain all of their pizzas and calzones will sell out. Pizzas can be sold for a profit of $3.50 and use 500 grams of dough, 300 grams of sauce, and 150 grams of cheese. Calzones can be sold for a profit of $2.50 and use 750 grams of dough, 200 grams of sauce, and 250...
Some Extra Definitions Recall that, for a nonrandom real number c, and a random variable X, we have Var (cX) = e Var (X). In this problem we'll generalize this property to linear combinations! Let be a vector of real nonrandom numbers, and let be a vector of random variables (sometimes called a random vector). Last, define the covariance matrix to be the matrix with all the covariances ar- ranged into a matrix. When we talk about taking the taking...
Wages (W) and years of education (X) have the following joint
distribution: The fractions in the table are probabilities. That
is, each cell is the probability that the row and column outcome
happen at the same time. • (4 points) Find the marginal probability
distribution for wages W. Hint: W takes on four values, you need to
find the probability that it equals each one. • (4 points) Find the
marginal probability distribution function for education X. • (5
points)...
You flip a coin 100 times. Let X= the number of heads in 100 flips. Assume we don’t know the probability, p, the coin lands on heads (we don’t know its a fair coin). So, let Y be distributed uniformly on the interval [0,1]. Assume the value of Y = the probability that the coin lands on heads. So, we are given Y is uniformly distributed on [0,1] and X given Y=p is binomially distributed on (100,p). Find E(X) and...
4. (20 points) Xavier and Yvette are real estate agents. Let X denote the number of houses that Xavier will sell in a month and let Y denote the number of houses Yvette will sel in a month with the following joint probabilities of (x, Y) 0.2 0.1 0.3 0.1 0.2 (a) Find the unconditional mean E (Y) (b) Find the unconditional variance V (Y) (c) Find the conditional means E (Y(X 0) and E (Y(X (d) Find COV (x,y)...