I have attached the assignment

Solution 1:
Consider the following table:
We know,
Therefore,
Expected value is calculated as follows:
Solution 2:
Probability for any event on roll of die
Ifcomes,
The pdf table is given as follows:
Expected value
=$0.33
Thus, expected value is $0.33.
Solution 3:
We know there are fixed independent trails and probability of each question is for every question. Thus, this follows Binomial distribution.
Student need to pass the test it means at least question need to be correct.
Thus, the probability that at least questions are correct,
Solution 4:
Random Variable X has uniform distribution.
Thus, Xunif (1.5,4.5)
Thus, pdf is given as
(a)
(b)
Thus,
(c)
The 90th percentile is given as follows:
Solution 5:
Let X be a random variable has exponential distribution.
Thus,
(a)
(b)
(c)
70th percentile is calculated as...