5. The amount of bread (in hundreds of kilos) that a bakery sells in a day...
The amount of bread (in hundreds pounds) x that a certain bakery is able to sell in a day is found to be a numerical value random phenomenon with probabilitydensity f(x) given byf(x)=kx for 0<=x,5=k(10-x) for 5<=x<10=0 else whereSo, find k and hence find the probability that the number of pounds of bread that will be sold tomorrow is
Bakery ABC sells bread for $2.1 per loaf that costs $0.78 per loaf to make. Bakery ABC knows that at the end of the day, he can sell all remaining bread for $0.45. Assuming Bakery ABC behaves optimally, what is the probability he would have a stockout each day? Note: If your answer is 12.345%, record 0.1235
3. Peterson's Bakery makes bread using two inputs: workers and machinery (ovens). In the short-run, the relationship between the number of workers and the bakery's output (loaves of bread) in a given day is as follows: Number of Workers Total Physical Product of Labor Marginal Physical Product of Labor 0 A5 65 80 85 6 82 a. (1.5 pt) Complete the Marginal Physical Product of Labor column in the table above and indicate each of the following regions (IMR, DMR,...
15. Let X and Y denote the lengths of life, in hundreds of hours, for co ponents of typesI and types II, respectively in an electronic system. The joint density of X and Y is given by Bre" (z +v)/2 f(z, y) = otherwise Find the probability that a component of type II will have a life lenght in excess of 200 hours. 16. Let the random variables X and Y have the joint p.d.f a. f(z,y)=ī, for (z,y) =...
Example 7 The amount of electricity (in hundreds of kilowatt-hours) that a certain power company is able to sell in a day is found to be a random variable with the following probability density function (pdf): kx k(10-x): 0: 0sxs5 5 x 10 elsewhere n) = (i) (ii) Find the value of k. What is the probability that the amount of electricity that will be sold is more than 600 kilowatt-hours. (ii) What is the probability that the amount of...
5. Let the joint probability density function of X and Y be given by, f(x,y) = 0 otherwise (a) Find the value of A that makes f (x, y) a proper probability density function (b) Calculate the correlation coefficient of X and Y. (c) Are X and Y independent? Why or why not?
5. Let X and Y be independent and identically distributed with marginal probability density function İf a> 0, otherwise, e-ea f(a)-( where >0 (a) [6 pts] Use the convolution formula to find the probability density function of X +Y (b) (6 pts) Find the joint probability density function of V= X + Y U=X+Y and
5. Let X and Y be independent and identically distributed with marginal probability density function İf a> 0, otherwise, e-ea f(a)-( where >0 (a) [6...
3.5. Suppose that X and Tare independent, continuous random variables and that U-X+1. Denote their probability density functions by f(x), g(y) and h(u) and the corresponding cumulative probability functions by F(x), G(2) and H(u) respectively. Then For a fixed value of I, say T-y,this probability is F(u-), and the probability that I will lie in the range y to y+dy is g()dy. Hence the probability that Usu and that simultaneously Y lies between y and y+dy is F(u-)go)dy and so...
Exercise 5(SOA). A car dealership sells 0,1, or 2 cars on any day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car. Let X denote the number of luxury cars sold in any given day and let y denote the number of extended warranties sold. We have: 1 12 P(X = 0, = 0) = 5; P(X = 1, Y = 0) = 12, P(X = 2, Y =...
3. Let X denote the temperature (°C) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density for (X,Y) is given by fxy(x, y) = c(4x + 2y + 1),0 < x < 40,0 < y = 2 (a) Find the value of c that makes this joint density legitimate. (b) Find the probability that on a randomly selected day the air...