SOLUTION: A random variable X follows the continuous uniform distribution with a lower bound of −2 and an upper bound of 19.
a). Calculate P(X ≤ 1). (Round intermediate calculations to
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a). Calculate P(X ≤ 1). (Round intermediate calculations to
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Question 1153486: A random variable X follows the continuous uniform distribution with a lower bound of −2 and an upper bound of 19.
a). Calculate P(X ≤ 1). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
You can put this solution on YOUR website! let x be the lower bound and y be the upper bound
:
f(a) = 1/(y-x), f(a) = the probability density function. For x≤ a ≤y.
:
f(a) = 1/(19-(-2)) = 1/21 = 0.047619
:
integrate f(a), which equals 0.047619 * x
:
evaluate the integral of f(a) from -2 to 1
:
P(X ≤ 1) = (0.047619 * 1) - (0.047619 * (-2)) = 0.047619 + 0.095238 = 0.142857 is approximately 0.1429
:
The segment, where the random variable X varies, has the length of (19-(-2)) = 21.
The length of the segment [-2,1] is 3 units.
Therefore, the probability under the question is
P(X <= 1) = = = 0.1429. ANSWER
