where 0 x < oo and 0> 0. e is a parameter of the exponential distribution, a fixed constant that controls the shape and variability of the probability density function. Note that each value of e generates a distinct exponential distribution The mean of a probability density function is referred to as its expected value. We can use the integral to calculate the expected value, denoted E(f) E(f)xf(x)dx The variance of a probability density function describes the variability of the distribution. The variance, denoted V(f), can also be calculated using the integral v) Ef2)-E)
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!
How are the mean and variance of an exponential random variable related? *requires integration by parts? More information is given in the picture but this is the question i am trying to answer. I really would appreciate clean handwriting in the answer as a lot of answers and variables are too difficult for me to follow
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