550.310 Probability & Statistics - SPRING 2012 MIDTERM 1
SOLUTION
1. (a) An experiment consists of rolling a single 6-sided die 10
times in a row and noting the sequence ofup-faces. How many
sequences are possible? ANSWER: 610.(b) (continued) How many
sequences have exactly three6s? ANSWER:
103
57.
(c) (continued) Assume the die is balanced. Given that there are
exactly three 6s in the sequence, what isthe probability that all
three occur consecutively? ANSWER: 85
7
(103
)57 = 8120 =
115 .
2. Suppose X and Yare jointly continuous random variables with
the following joint probability densityfunction:
f(x, y) =
2xy4 if 1< x
8/13/2019 310sp12_midterm1sol.pdf
2/2
(b) Consider the jointly discrete random variables XandYhaving
the joint p.m.f. given in the table below:
Use this table to compute the following probabilities (clearly
label each calculation):P(1 X 2, Y >2), P(X > Y), P(X Y), and
P(1 X 2|Y >2).
