[Joint PDFS will be covered in Week 7] Assume that X and Y represent the percentage of time in a certain day that Machines A and B are busy in a production line. The joint PDF of these random variables is given by fy y(x,y) = (6x + 5y) where 0sxs1 and 0sys1. (a) The marginal density of X is given by (select one choice and fill in the box): a (Type your answer as a function of x or y and in a form similar to as needed. Do not convert fractions to decimals.) C+ X+ or d. O A. fx(x) = for 0sxs1 OB. fy(y) = for 0sys1 (b) The marginal density of Y is given by (select one choice and fill in the box). C. or a as needed Do not convert fractions to decimals) C+ (Type your answer as a function of x or y and in a form similar to O A. fy(y) = for 0sys1 OB. fx(x) = for 0 sxs1 (c) What is the probability that Machine A will be busy less than one-third of the day? This probability is (Type an integer or a simplified fraction. Do not convert fractions to decimals)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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