1. Define the following terms: random variable, probability density function, expected value.
   
2. Suppose that ships arrive at a port at an average rate of 1 per day.
   (a) What is the probability that more than two ships will arrive on the same day? State any assumptions you make.
   (b) What is the probability that this will happen on more than two days next week?
   
3. If the percent yield from Process A has mean 68 and standard deviation 3, while the percent yield from Process B has mean 74 and standard deviation 3, and you do one run of each process, what is the probability that Process A gives a higher yield than Process B? State any assumptions you make. [Hint: Find the mean and variance of Y_A-Y_B, where Y_A and Y_B are the yields from Process A and Process B, respectively, and compute P(Y_A-Y_B > 0). Note that F(1.414) = 0.9214.]
   
4. If a random variable X can take values 1, 2, 4, 8 with probabilities 0.6, 0.05, 0.05, 0.3, respectively, plot the probability density function and find the mode, median, mean, variance and standard deviation of X. If you know that X is greater than 1, what is the probability that X is greater than 7?
   
5. You are planning a survey to study the concentration of arsenic in the buffering material on the ground underneath public playgrounds build with CCA pressure-treated wood. The buffering material could be sand, pea gravel, mulch, or shredded tires. What measurements would you make? List at least 6 factors that might explain any variability in your results.

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Statistics 3N03