What is the expected value E(X) for this distribution
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!
Random Variable: A random variable is a real valued function that assign a real number to each outcome (i.e., sample point) of a random experiment. Random variable divided into two types they are
- Discrete random variable - A random variable say "x", which can take finite number of values in the interval of domain
- Continuous random variable - A random variable say "x", which can take any value in its domain or in an interval.
The Mean (expected value) of the random variable x is denoted by E[X]
i.e., E[X] =
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