(Uniform) Suppose X follows a continuous uniform distribution from 4 to 11. (a) Write down the PDF of X. (b) Find P(X ≤ 7). Round your answer to 4 decimals. (c) Find P(5 < X ≤ 7). Round your answer to 4 decimals. (d) Determine the conditional probability P(X > 5 | X ≤ 7). Round your answer to 4 decimals.

a)

b)

c)

d)

And we can find this probability with this formula from the Bayes theorem:

Step-by-step explanation:

For this case we assume that the random variable X follows this distribution:

Part a

The probability density function is given by the following expression:

Part b

We want this probability:

And we can use the cumulative distribution function given by:

And replacing we got:

Part c

We want this probability:

And we can use the CDF again and we have:

Part d

We want this conditional probabilty:

And we can find this probability with this formula from the Bayes theorem: