1. The cumulative probabilities for a continuous random variable X are P(X 10) = 0.42 and P(X 20) = 0.66. Calculate the following probabilities.

a. P(X > 10)

b. P(X > 20)

c. P(10 < X < 20)

2. For a continuous random variable X with an upper bound of 4, P(0 X 2.5) = 0.54 and P(2.5 X 4) = 0.16. Calculate the following probabilities.

a. P(X < 0)

b. P(X > 2.5)

c. P(0 X 4)

3. For a continuous random variable X, P(20 X 40) = 0.15 and P(X > 40) = 0.16. Calculate the following probabilities.

a. P(X < 40)

b. P(X < 20)

c. P(X = 40)

4. A random variable X follows the continuous uniform distribution with a lower bound of 5 and an upper bound of 35.

a. What is the height of the density function f(x)?

b. What are the mean and the standard deviation of the distribution?

c. Calculate P(X > 10).