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Using Technology In Exercises 17-22, use a symbolic
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Calculus: An Applied Approach (MindTap Course List)
- Average Traffic Spacing The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per flour, the probability P that the headway is at least t seconds is given by P=0.87t. a. What is the limiting value of P? Explain what this means in practical terms. b. The headway h can be calculated as the quotient of the spacing f, in feet, which is the average distance between vehicles, and the average speed v, in feet per second, of traffic. Thus, the probability that spacing is at least f feet is the same as the probability that the headway is at least f/v seconds. Use function composition to find a formula for the probability Q that the spacing is at least f feet. Note: Your formula will involve both f and v. c. If the average speed is 88 feet per second 60 miles per hour, what is the probability that the spacing between two vehicles is at least 40 feet?arrow_forwardD6) Finance Suppose that the stock price follows geometric Brownian motion dXt = 0.04 Xt dt + 0.2 Xt dWt. Write the probability density function for the distribution of the stock prices in 2 years if the current stock price is 80.arrow_forwardMarketing estimates that a new instrument for the analysis of soil samples will be verysuccessful, moderately successful, or unsuccessful, with probabilities 0.3, 0.6, and 0.1,respectively. The yearly revenue associated with a very successful, moderatelysuccessful, or unsuccessful is $10 million, $5 million, and $1 million, respectively. Let therandom variable X denote the yearly revenue of the product. Determine:a) the mass function of X;b) the mean of X; andc) the variance of X.arrow_forward
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