Question

Let X ∼ Unif[4, 10]. Calculate P(X < 6).

Answer 1

To calculate P(X < 6) for a uniform distribution from 4 to 10, we find the probability of getting a value less than 6. The probability is 0.3333.

Step-by-step explanation:

To calculate P(X < 6) for a random variable X that follows a uniform distribution from 4 to 10, we need to find the probability of getting a value less than 6.

Since X is a continuous random variable, we calculate the probability by finding the area under the probability density function (PDF) curve between 4 and 6. For a uniform distribution, the PDF is a constant value within the interval of interest.

The formula to calculate the probability is P(X < 6) = (6 - 4) / (10 - 4) = 2 / 6 = 1/3 = 0.3333.