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A dart is thrown at a number line in such a way that it always lands in
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Calculus and Its Applications (11th Edition)
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- A dart is thrown at a number line in such a way that it always lands in the interval [0,10]. Let x represent the number that the dart hits. Suppose that the probability density function for x is given by the following function. 1 f(x) = 50x, for 0≤x≤ 10 Find P(6 ≤x≤ 10), the probability that the dart lands in [6,10]. How is the probability that the dart lands in [6,10] found? 1 O A. Integrate 50x twice, then evaluate the integral over the limits 6 and 10. 1 O B. Evaluate the expression 50x over the limits 6 and 10, then subtract. 1 OC. Evaluate the expression over the limits 6 and 10, then add. 1 ⒸD. Integrate 50x, then evaluate the integral over the limits 6 and 10. P(6≤x≤ 10) = (Type an integer or a simplified fraction.) Carrow_forwardAssume that the box contains 12 markers: 8 that contain ink and 4 that do not contain ink. A sample of 7 markers is selected and a random variable YY is defined as the number of markers selected which do not have ink. Fill in the table below to complete the probability density function. Be certain to list the values of Y in ascending order.arrow_forwardLet y be the random variable with the time to hear an owl from your room's open window (in hours). Assume that the probability that you still need to wait to hear the owl after y hours is one of the following: the probability is given by 0. 47e-4y + 0. 52e-5y Find the probability that you need to wait between 2 and 4 hours to hear the owl, compute and display the probability density function graph as well as a histogram by the minute. Compute and display in the graphics the mean, variance, and quartiles of the waiting times. Please pay attention to the various units of time!arrow_forward
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