QUESTION 8 Which of the following is TRUE if random variables X and Y are statistically dependent on each other. 0 f(y|x) = h(y) for all (x,y) O f(le) = 900 for 3" (MI) 0 they) = 9(X)h(Y) for 3" (MI) The conditional probabilities for X change as the value of Y varies AND vice-versa. Also, the marginal distribution for X does not equal the conditional distribution for X for all Y values. Furthermore, the marginal distribution for Y does not equal the conditional distribution for Y for all X values. QUESTION 9 Let X = the high temperature in degrees Fahrenheit on a random day in Chicago and Y = the number of ice cream cones sold at a local ice cream shop. The relationship between X and Y is modeling using joint distribution f(x,y). The high temperature on a given Autumn day is known to be 50 degrees. In order to make a decision about whether or not to open the ice cream shop on that day, the owner would like to know the probability of selling more than 100 ice cream cones on that day. How woud this calculation be made? 0 First integrate f(x,y) over all x to find g(x). Then determine fy(y|x) as f(x,y)/g(x) evaluated at x=50. Finally, integrate fy(y|50) for y>100 to determine the probabilty in question. 0 First integrate f(x,y) over all y to find h(y). Then determine fx(x|y) as f(x,y)/h(y) evaluated at y=100. Finally, integrate fx(x|100) for x>50 to determine the probabilty in question. 0 Integrate f(x,y) for x>50 and y>100 to determine the probabilty in question. 0 First integrate f(x,y) over all y to find h(y). Then integrate h(y) for y>100 to determine the probabilty in question. QUESTION 10 Let X = the high temperature in degrees Fahrenheit on a random day in Chicago and Y = the number of ice cream cones sold at a local ice cream shop. In order to analyze the relationship between X and Y, a joint distribution f(x,y) will be used as a model. Which of the options below correctly answer the following question AND provide valid justication: Should the joint distribution have the property f(x,y) = g(x)h(y), where g(x) and h(y) are the marginal distributions? 0 No, because it is known that lower values of X directly cause lower values of Y. O Yes, because X and Y are statistically independent. 0 No, because X and Y are statistically dependent on each other. 0 Yes, because X and Y are statistically dependent on each other