The continuous random variable X, follows uniform distribution, that is X ~ U (0,23), find P(2<X<18)?
Question
Solution
The probability for a continuous uniform distribution between two points can be calculated using the formula:
P(a < X < b) = (b - a) / (B - A)
where:
- A and B are the parameters of the distribution (in this case 0 and 23 respectively), and
- a and b are the points of interest (in this case 2 and 18 respectively).
Substituting the given values into the formula, we get:
P(2 < X < 18) = (18 - 2) / (23 - 0)
This simplifies to:
P(2 < X < 18) = 16 / 23
So, the probability that the random variable X falls between 2 and 18 is 16/23.
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