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The continuous random variable X, follows uniform distribution, that is X ~ U (0,23), find P(2<X<18)?  16/238/2318/239/23

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Solution

The probability P(2<X<18) for a continuous uniform distribution can be found by calculating the length of the interval (18-2) and dividing it by the total length of the distribution (23-0).

Step 1: Calculate the length of the interval The length of the interval is the upper limit minus the lower limit. In this case, it's 18 - 2 = 16.

Step 2: Calculate the total length of the distribution The total length of the distribution is the upper limit minus the lower limit. In this case, it's 23 - 0 = 23.

Step 3: Divide the length of the interval by the total length of the distribution The probability is the length of the interval divided by the total length of the distribution. In this case, it's 16 / 23.

So, P(2<X<18) = 16/23.

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