Suppose x is a uniform random variable with c=10 and d=90. Find the probability that a randomly selected observation exceeds26.
0.8
4.0
To find the probability that a randomly selected observation exceeds 26, we need to find the area under the probability density function (PDF) curve for values of x greater than 26.
The PDF of a continuous uniform distribution is given by:
f(x) = 1 / (d - c)
where c is the lower limit and d is the upper limit of the distribution.
In this case, c = 10 and d = 90. Therefore, the PDF is:
f(x) = 1 / (90 - 10) = 1 / 80
To find the probability of x exceeding 26, we need to integrate the PDF from 26 to 90:
P(x > 26) = ∫[26, 90] f(x) dx
P(x > 26) = ∫[26, 90] (1 / 80) dx
P(x > 26) = [x / 80] from 26 to 90
P(x > 26) = (90 / 80) - (26 / 80)
P(x > 26) = 0.1125
Therefore, the probability that a randomly selected observation exceeds 26 is 0.1125 or 11.25%.
To find the probability that a randomly selected observation from a uniform random variable exceeds a certain value, we can use the formula for the cumulative distribution function (CDF) of a uniform distribution.
The CDF of a uniform distribution is given by:
F(x) = (x - c) / (d - c)
where x is the value of the observation, c is the lower bound of the distribution, and d is the upper bound of the distribution.
In this case, the lower bound (c) is 10 and the upper bound (d) is 90.
To find the probability that a randomly selected observation exceeds 26, we need to calculate 1 - F(26).
F(26) = (26 - 10) / (90 - 10)
= 16 / 80
= 0.2
So, P(x > 26) = 1 - F(26) = 1 - 0.2 = 0.8.
Therefore, the probability that a randomly selected observation from the given uniform distribution exceeds 26 is 0.8.