Calls to the 24-hour customer support line for Richman Financial Services occur randomly following a Poisson distribution with the following average rates during different hours of the day:

3. A Bloomberg Businessweek North American subscriber study collected data from a sample of 2861 sub-scribers. Fifty- nine percent of the respondents indicated an annual income of $ 75,000 or more, and 50% reported having an American Express credit card. a. What is the population of interest in this study? b. Is annual income a categorical or quantitative variable? c. Is ownership of an American Express card a categorical or quantitative variable? d. Does this study involve cross- sectional or time series data? e. Describe any statistical inferences Bloomberg Businessweek might make on the basis of the survey.Time Period Avg Calls Per Hour Time Period Avg Calls Per Hour Midnight - 1 a.m. 2 Noon - 1 p.m. 35 1 am. - 2 a.m. 1 p.m. - 2 p.m. 20 2 am. - 3 am. 2 p.m. - 3 p.m. 20 3 am - 4 a.m. 3 p.m. - 4 p.m. 20 4 am. - 5 am. 4 4 p.m. - ) p.m. 18 5 am. - 6 a.m. 5 p.m. - 6 p.m. 18 6 am - 7 am. 12 6 p.m. - 7 p.m. 15 7 am. - 8 a.m. 18 7 p.m. - 8 p.m. 10 8 am. - 9 am. 25 8 p.m. - 9 p.m. 6 9 am - 10 a.m. 30 9 p.m. - 10 p.m. 10 am. - 11 a.m. 25 10 p.m. - 11 p.m. 4 11 am. - Noon 20 11 p.m. - Midnight2\fPlayer LeBron Kobe Steph Michael Others James Bryant Curry Jordan NBA 20% 30% 15% 19% 16% Percentages Observed 23 28 10 15 11 Counts Michael wants to carry out a statistical inference procedure for this scenario using the X"-distribution. Which of the following conditions must be met? (Select all that apply.) There must be at least 10 successes and 10 failures for each level of the categorical variable. There must be an expected count of at least 5 for each level of the categorical variable. The sample size must be at least 30 or the population data must be normally distributed. The difference in all calculated proportions must be at least 5. The observations must be independent. There must be at least 3 levels of the categorical variable.Let X1 and X2 be independent random variables having the standard normal distribution. Obtain the joint Lebesgue density of (Y1, Yz), where Yi = VX?+ X} and Y2 = X1/X2. Are Y1 and Y2 independent? Note. For this type of problem, we may apply the following result. Let X be a random k-vector with a Lebesgue density fx and let Y = g(X), where g is a Borel function from (R*, B* ) to (R*, B*). Let A1, . .., Am, be disjoint sets in B* such that R* - (Aj U . . . U Am,) has Lebesgue measure 0 and g on A; is one-to-one with a nonvanishing Jacobian, i.e., the determinant Det(Og(x)/Or) # 0 on Aj, j =1. .... m. Then Y has the following Lebesgue density: fy (x) = >Det (Oh, (x)/ar) | fx (h,(r)). j=1 where h, is the inverse function of g on A;, j = 1, ..., m