A company measures the quality of its products using two continuous random variables: X: the standardized thickness of a manufactured sheet,Y: the standardized strength of the sheet. The joint probability density function of X and Y is given as Show your work on the scratch paper when answering Q23-25 below. X

Compute the conditional probability P(X>1.5∣X>1). Provide three digits after the decimal point.

Given that a startup receives a positive evaluation, what is the probability that it will actually be successful? Provide six digits after the decimal point.

What is the probability that a student who knows R also knows at least one of the other two languages? Compute three digits after the decimal point.

A venture capital firm evaluates thousands of startup companies each year. Historically, only 1 out of every 1,000 startups turns out to be successful. The firm uses an initial evaluation test to assess potential. The evaluation test is imperfect: If a startup will be successful, the test returns a positive evaluation with probability 0.8 If a startup will not be successful, the test returns a positive evaluation with 0.05 Show your work on the scratch paper answering Q4-Q6.

A factory produces metal rods whose weights (in pounds) are independent and identically distributed random variables with mean μ = 5 and standard deviation σ = 0.2. The rods are packaged in boxes of 30. Show your work on the scratch paper answering Q16-Q17.

A graduate-level statistics class surveyed 120 students on their knowledge of three software tools: R, Python, and MATLAB. 65 students know R 75 students know Python 50 students know MATLAB 30 students know both R and Python 25 students know both R and MATLAB 35 students know both Python and MATLAB 15 students know all three languages Show your work on the scratch paper when answering Q1-Q3.

The Open/Closed Principle calls for adding new code/functionality without modifying the existing code. What is the benefit from doing so?  

What is the output of the code below? Explain the observed behavior in detail. Map a = new HashMap(); Map b = new HashMap(); a.put(“c”, 130); b.put(“c”, 130); System.out.println(a.get(“c”) == b.get(“c”)); // output:

What is the output of the code below? Explain the observed behavior in detail. String s1 = “hello”; String s2 = “hello”; System.out.println( s1 == s2 ); // output: