Which of the following diseases results from vitamin C deficiency?

Which of the following is NOT a role of water?

Which of the vitamins is most likely to toxic affects?

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.