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1) What is the expected "winnings" for a single card draw in the following game?

Card, x_i 2 to 10 Jack, Queen, King Ace

X(x_i) Lose $3 Win $5 Win $10

P(x_i)

2) For the sequential search algorithm, if the probability of a successful search is 0.8, then what is the expected number of comparisons for a search?

x_i L₁ L₂ L₃ . . . L_n-1 L_n Unsuccessful search

X(x_i)
number of comparisons

P(x_i)

3) For the following relations on the set of integers, determine which properties hold for each relation:

Relation Properties on Relations

reflexive symmetric transitive antisymmetric

R₁:

R₂:

R₃:

R₄:

R₅:

Card, x_i	2 to 10	Jack, Queen, King	Ace
X(x_i)	Lose $3	Win $5	Win $10
P(x_i)

Relation	Properties on Relations
Relation	reflexive	symmetric	transitive	antisymmetric
R₁:
R₂:
R₃:
R₄:
R₅: