Consider a random variable X that has a pdf ,0sxs1 f(x)={2-x, 1
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!
![Consider a random variable X that has a pdf
,0<x<1
f(x)={2-x , 1<x<2
, otherwise
This pdf is of a triangular distribution. Use the inverse transformation technique to generate the triangular random variate X
in terms of a uniform random number R-[0,1]. Fill in the equations below using the math editor. (Click the red symbol to open up
the math editor.)
O<R<0.5
X =
0.5 <R<1
Generate a triangular random variate using the uniform random number 0.4256
The triangular random variate is:
V (Here, you may directly fill in the value without using the math editor.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a742d41-007a-4c51-8e14-f185abf29807%2Fa8189517-19fa-400e-aec4-64ad8912c48b%2Fhq30698_processed.png&w=3840&q=75)
Step by step
Solved in 2 steps with 2 images
