Step-by-step solution

1. Step 1 of 5

   The cumulative distribution function for the known data is,

   

   The resultant cumulative distribution function of X is,

   

   Comment

2. Step 2 of 5

   (a)

   Using the cumulative distribution function, the required probability is,

   

   Comment

3. Step 3 of 5

   (b)

   Using the cumulative distribution function, the required probability is,

   

   Comment

4. Step 4 of 5

   (c)

   Using the cumulative distribution function, the required probability is,

   

   Comments (4)

5. Step 5 of 5

   (d)

   Using the cumulative distribution function, the required probability is,

   

   Comment