Review for the Final Exam (STA255)

1. (a) Review the midterm test, in class examples, homework problems;

(b) Review the density functions, mgfs for the distributions we covered

(both discrete and continuous). Review the methods of finding

expectations and variances straightforward and using mgfs.

(c) Review how t, F, 𝜒2 distributions were defined, make sure you

know how to use the corresponding tables.

2. Urn I contains two white balls and two black balls; urn II contains three

white and two black balls. One ball is randomly transferred from I to II.

Then one ball is drawn from II and it turns out to be white. What is the

probability that the transferred ball was white?

3. The letters of CONSPICUOUS are arranged randomly. What is the

probability that P will appear in the position directly in front of I?

4. Suppose we have a bowl with 10 marbles - 2 red marbles, 3 green

marbles, and 5 blue marbles. We randomly select 4 marbles from the

bowl, with replacement. What is the probability of selecting 2 green

marbles and 2 blue marbles?

5. If electricity power failures occur according to a Poisson distribution

with an average of 3 failures every twenty weeks, calculate the

probability that there will not be more than one failure during a

particular week.

6. The weight (in pounds) of «medium-size» watermelons is normally

distributed with mean 15 and variance 4. A packing container for

several melons has a nominal capacity of 140 pounds. What is the

maximum number of melons that should be placed in a single packing

container if the nominal weight limit is to be exceeded only 5% of the

time?

7. Let Y~Unif(0, 5) and 𝑈 = −𝑌2. Find 𝐹𝑈(𝑢).