Most computer languages include a function that can be used to generate random numbers. In MS Excel, the RAND Function can be used to generate random numbers between zero and one. If we let x Denote a random number generator using RAND, Then X is the continuous random variable with the following probability density function. f(x) = 1 for 0 ≤ x ≤ 1 0 Elsewhere a) Graph the probability density function. b) What is the probability of generating a random number between .25 and .75? c) What is the probability of generating a random number with a value less than or equal to 0.30? d) What is the probability of generating a random number with the value Greater than 0.60?
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!
14. Most computer languages include a
MS Excel, the RAND Function can be used to generate random numbers between zero and one.
If we let x Denote a random number generator using RAND, Then X is the continuous random
variable with the following
f(x) = 1 for 0 ≤ x ≤ 1
0 Elsewhere
a) Graph the probability density function.
b) What is the probability of generating a random number between .25 and .75?
c) What is the probability of generating a random number with a value less than or equal to
0.30?
d) What is the probability of generating a random number with the value Greater than 0.60?
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