Question

A random variable follows the continuous uniform distribution

between 30 and 50.
a. Calculate the following probabilities below for the
distribution.
1. P(x ≤ 45)
2. P(xs 35)
3. P(x ≤ 40)
4. P(x =

Answer 1

When dealing with continuous random variables, we calculate the probability that the variable falls within a certain range rather than the probability of it taking on a specific value. The probabilities P(x < c) and P(x ≤ c) are equivalent for a continuous random variable. To find P(x > 5), you can subtract P(x < 5) from 1.

Step-by-step explanation:

When dealing with continuous random variables, we calculate the probability that the variable falls within a certain range rather than the probability of it taking on a specific value. This is because the probability of a continuous random variable taking on a specific value is always 0.

For a continuous random variable, the probabilities P(x < c) and P(x ≤ c) are equivalent because the probability of the variable taking on a specific value is 0, making the difference between < and ≤ negligible.

To calculate P(x > 5) for a continuous probability function, we can subtract P(x < 5) from 1, since the total probability of a continuous probability function is always 1.