At a crime scene, a forensic technician found the body temperature of the victim was 33 degree celcius at 6:00 pm. One hour later, the coroner arrived and found the body temperature of the victim fell to 31.5 degree celcius. The forensic technician determined that the change in the atmospheric temperature could be modelled satisfactorily as 20e^-.02t in the time window of +3 hours starting at 6:00 pm. It is known that the body temperature of alive person is 37 degree celcius. When was the victim murdered?
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!
At a crime scene, a forensic technician found the body temperature of the victim was 33 degree celcius at 6:00 pm. One hour later, the coroner arrived and found the body temperature of the victim fell to 31.5 degree celcius. The forensic technician determined that the change in the atmospheric temperature could be modelled satisfactorily as 20e^-.02t in the time window of +3 hours starting at 6:00 pm. It is known that the body temperature of alive person is 37 degree celcius. When was the victim murdered?
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