The particle size distribution is an important factor in solid missile.In production, there are some significant problems when the particle sizes are too large. According to past studies, it has been determined that the particle size (in micrometers) distribution is characterized by the following function. 2x3. x>1 f(x) = { 0, elsewhere (a) Verify that this is a valid density function. (b) Evaluate F(x). (c) What is the probability that a random particle from the manufactured fuel exceeds 7 micrometers? (a) The function f(x) is a valid density function because V for all V and because f(x) dx = - 3dx = (D -0 -0- O xs1, (b) F(x) = O x>1. (c) P(X > 7) =O (Type an integer or decimal rounded to four decimal places as needed.)
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!
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