For Physics students. In Probability, the exponential probability distribution dP function is defined by Aet where...
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For Physics students. In Probability, the exponential probability distribution dP function is defined by Aet where dt is a positive constant. A particular application of this distribution is to the decay of radioactive nuclei. In that case, the probability that a particular nucleus will decay at some time T in the interval from t=0 to t=t is given by P(0 ≤T≤t) = [e¹ dt. (a) Show that the p.d.f. dP dt = λe=2t is well defined i.e. show that he dt = 1. (b) Evaluate P(0 ≤ T ≤t) = λe-¹¹ dt. (c) The probability that a particular nucleus will decay { = within a time interval called the half-life is ½. Deduce that the half-life is given by In 2 . (d) Using your answer to (b) in the case where λT < < <1, explain why the 2 constant λ is called the probability of decay per unit time. (Hint: Do a MacLaurin expansion of the answer in (b).) For Physics students. In Probability, the exponential probability distribution dP function is defined by Aet where dt is a positive constant. A particular application of this distribution is to the decay of radioactive nuclei. In that case, the probability that a particular nucleus will decay at some time T in the interval from t=0 to t=t is given by P(0 ≤T≤t) = [e¹ dt. (a) Show that the p.d.f. dP dt = λe=2t is well defined i.e. show that he dt = 1. (b) Evaluate P(0 ≤ T ≤t) = λe-¹¹ dt. (c) The probability that a particular nucleus will decay { = within a time interval called the half-life is ½. Deduce that the half-life is given by In 2 . (d) Using your answer to (b) in the case where λT < < <1, explain why the 2 constant λ is called the probability of decay per unit time. (Hint: Do a MacLaurin expansion of the answer in (b).)
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Quantitative Methods for Business
ISBN: 978-0324651751
11th Edition
Authors: David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey cam
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