Uniform Distribution A uniform distribution is a continuous probability distribution for a random variable x between two values a and b ( a < b ) , where a ≤ x ≤ b and alt of the values of x are equally likely to occur. The graph of a uniform distribution is shown below. The probability density function of a uniform distribution is y = 1 b − a on the interval from x = a to x = b. For any value of x less than a or greater than b, y = 0. In Exercises 59 and 60, use this information. 60. For two values c and d. where a ≤ c < d ≤ b, the probability that x lies between c and d is equal to the area under the curve between c and d. as shown below. So, the area of the red region equals the probability that x lies between c and d. For a uniform distribution from a = 1 to b = 25, find the probability that (a) x lies between 2 and 8. (b) x lies between 4 and 12. (c) x lies between 5 and 17. (d) x lies between 8 and 14.
Uniform Distribution A uniform distribution is a continuous probability distribution for a random variable x between two values a and b ( a < b ) , where a ≤ x ≤ b and alt of the values of x are equally likely to occur. The graph of a uniform distribution is shown below. The probability density function of a uniform distribution is y = 1 b − a on the interval from x = a to x = b. For any value of x less than a or greater than b, y = 0. In Exercises 59 and 60, use this information. 60. For two values c and d. where a ≤ c < d ≤ b, the probability that x lies between c and d is equal to the area under the curve between c and d. as shown below. So, the area of the red region equals the probability that x lies between c and d. For a uniform distribution from a = 1 to b = 25, find the probability that (a) x lies between 2 and 8. (b) x lies between 4 and 12. (c) x lies between 5 and 17. (d) x lies between 8 and 14.
Solution Summary: The author explains that the probability of x lies between 2 and 8 is 0.25, and the required probability is obtained by finding the area of the red region.
Uniform DistributionA uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a < b), where a ≤ x ≤ b and alt of the values of x are equally likely to occur. The graph of a uniform distribution is shown below.
The probability density function of a uniform distribution is
y
=
1
b
−
a
on the interval from x = a to x = b. For any value of x less than a or greater than b, y = 0. In Exercises 59 and 60, use this information.
60. For two values c and d. where a ≤ c < d ≤ b, the probability that x lies between c and d is equal to the area under the curve between c and d. as shown below.
So, the area of the red region equals the probability that x lies between c and d. For a uniform distribution from a = 1 to b = 25, find the probability that
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