Problem 4. In 2009 the LA Times Data Desk started its "Mapping LA" project, which included collecting information about all 114 distinct neighborhoods of the city of Los Angeles. The dataset we will work with in Problems 4-7 includes the 104 neighborhoods that, as of 2008, had at least one public school in the neighborhood. Here is some important information about the variables in the dataset: . Neighborhood: the name of the neighborhood * Income: the median income of the neighborhood's residents, in thousands of dollars . Schools: the median API score of schools in the neighborhood, measured on a scale from 2000 (bad) to 1000 (good) Asian corresponds to Asian 5) measured on a scale from 1 (not diverse at all) to 10 (very diverse) · Asian, Black, Latino, white: the percentage of residents with each of those ethnicities (i.e.,5% . Diversity: how likely neighborhood residents are to encounter a resident of a different ethnicity, . Population: the neighborhood's population, according to the 2000 U.S. Census, in thousands How many cases are in this dataset? Which variable is the label variable? categorica iable (circle one)? Is population a quantitative Was this dataset collected from an observational study (circle one)? experiment Which of the following plots would be useful for identifying the distribution of Income: (circle one)? histogram scatter plot pie chart

refer  to  image  below.

Please answer number 1,2 and 3

Teachers get courses assigned to teach each semester. For each instructor, there are the courses that the instructor can teach based on the skill set of the instructor, and there are courses that the teacher would rather teach all the time, closer to their specialization. To be able to teach in any department, a teacher must be able to teach more than the favorite courses. Let X denote the proportion of teachers who teach the whole spectrum of courses taught in a department, and Y the proportion of teachers who teach the courses they specialize in. Let X and Y have the joint density function : f(x,y)=2(x+y),0<y<x<1 (a) Given that 10% of the teachers teach the whole spectrum of courses, what is the probability that fewer than 5% teach their favorite courses? (b)  What is the expected percentage of teachers teaching their favorite courses when the proportion of teaching the whole spectrum is 0.7?