Determine the value for c and the covariance and correlation for the joint probability density function fxy (x, y) 0 < x < 3 and 0 < y < x. Round your answers to three decimal places (e.g. 98.765). = cxy over the range C = i Covariance = i Correlation = i

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Prob & Stat 1

Q. 2 Suppose I see students during regular office hours. Time spent with students follow an exponential distribution with mean of 20 minutes. (i) Write the probability density function of random variable X, E (X) and Var(X). (ii) Find the probability that a given student spends less than 0.4 hours with the professor. (iii) Find the probability that a given student spends between 0.20 and 0.5 hours with the professor. (iv) Find the probability that a given student spends at least 0.75 hours with the professor.