e moment generating function for X and Using this unction, compute the first and second moments of
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!
![) Let X be a random variable whose probability density function is
given by
+-e",x>0
fr(x)={
0,otherwise
Then Write down the moment generating function for X and Using this
moment generating function, compute the first and second moments of
X.
(ii) Find the first four moments about x = 10 for the series 4, 7, 10, 13,
16, 19, 22.
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