101. Suppose that P, the price of a certain commodity (in dollars), and S, its total sales (in 10,000 units), are ran- dom variables whose joint probability distribution can be approximated closely with the joint probability density 5pe s for 0.20 0 f(p,s) = elsewhere Find the probabilities that (a) the price will be less than 30 cents and sales will exceed 20,000 units; (b) the price will be between 25 cents and 30 cents and sales will be less than 10,000 units.
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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