Question

Find 6 f(x) dx 0 if f(x) = 4 for x < 4 x for x ≥ 4 .

Answer 1

The probability P(0 < x < 4) for a uniform distribution with f(x) = 1 from 0 to 10 is calculated as 0.4.

Step-by-step explanation:

The question asks to find the probability P(0 < x < 4) for a continuous probability distribution where the function is defined as f(x) = 1 for 0 ≤ x ≤ 10. This is an example of a uniform distribution, where the probability is constant across the interval. The probability is calculated by finding the area under the probability density function over the interval from 0 to 4.

To find P(0 < x < 4), we use the formula for the uniform distribution:

P(a < x < b) = (b - a) * (1/(high - low))

Here, a = 0, b = 4, low = 0, and high = 10. So, the probability is:

P(0 < x < 4) = (4 - 0) * (1/(10 - 0)) = 4/10 = 0.4

Thus, P(0 < x < 4) = 0.4.