Question

Suppose that a R.V. has a continuous distribution with a pdf f where f(x) = {(16x⁴)(x-2) for 0

Answer 1

The probability P(0 < x < 4) is 4.

Step-by-step explanation:

The given question is asking for the probability P(0 < x < 4) for a continuous probability distribution with a uniform distribution. In this case, the probability density function (pdf) is constant within the range of 0 ≤ x ≤ 10. To find the probability within a specific range, we can calculate the area under the pdf curve between the given values. Since the pdf is constant, the area under the curve can be calculated by multiplying the width of the range by the height of the pdf. In this case, the width is 4 - 0 = 4 and the height is 1, so the probability is P(0 < x < 4) = (4 - 0)(1) = 4.