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Random Sampling of Questions
1. The probability that rain is followed by rain is 0
.
8, a sunny day is followed
by rain is 0
.
6. Find the probability that one has two rainy days then two
sunny days.
2. Let:
f
(
x
) =
k

x

2

,
for
x
=

1
,
0
,
1
,
3
•
Find
k
so that
f
is a PDF.
•
Find the expected value of
X
.
•
Find the expected value of
X
2
.
3. A balanced die is tossed twice. Let
A
be the event that an even number
comes up on the ﬁrst toss. Let
B
be the event that an even number comes
up on the second. Let
C
be the event that the ﬁrst two tosses gave the
same number. Are
A,B,C
•
pairwise independent
•
independent?
4. State Bayes’ Theorem.
5. If
A,B
are independent prove that
A
0
and
B
0
are independent.
6. What is the diﬀerence between saying that
A,B,C
are independent events,
versus saying that
X,Y,Z
are independent random variables?
7. In a poker game, 5 cards are dealt from a deck of 52. What is the proba
bility of getting a fourofakind?
8. If the joint PDF is given by:
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This note was uploaded on 12/16/2011 for the course CS cs102 taught by Professor Rsharma during the Spring '11 term at IIT Kanpur.
 Spring '11
 rsharma

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