Compute the standard deviation of X.

Suppose that you are given the distribution functions of two random variables X and Y. If Cov(X,Y)=0, are X and Y independent? Answer True/False below and provide a supporting reason on your scratch paper. An answer without a reason will receive 0. If this is not sufficient to determine whether they are independent, choose False and explain why.

Let X be a continuous random variable with the following probability density function:

In a store, the number of patients arriving in one-hour window to an emergency clinic follows a Poisson distribution with rate 25/hour. With 20% probability, each patient requires an operating room for an emergency surgery. Compute the expected number of operating rooms required per hour at this emergency clinic and its variance. Show your work on your scratch paper. Expected total required operating rooms = Variance of total required operating rooms =

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.

Find the value of the constant k that makes f(x) a valid probability density function.

Are the events “knows R” and “knows MATLAB” independent? Answer True/False and justify your answer on the scratch paper. No points will be given without the justification.

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:

Why are long methods problematic? Provide 2 main reasons.

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