(The Allais Paradox) Suppose we are offered achoice between the following two lotteries:L1: With probability 1, we receive $1 million.L2: With probability .10, we receive $5 million.L2: With probability .89, we receive $1 million.L2: With probability .01, we receive $0.Which lottery do we prefer? Now consider the followingtwo lotteries:L3: With probability .11, we receive $1 million.L2: With probability .89, we receive $0.L4: With probability .10, we receive $5 million.L2: With probability .90, we receive $0.Which lottery do we prefer? Suppose (like most people), weprefer L1 to L2. Show that L3 must have a larger expectedutility than L4.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
(The Allais Paradox) Suppose we are offered a
choice between the following two lotteries:
L1: With
L2: With probability .10, we receive $5 million.
L2: With probability .89, we receive $1 million.
L2: With probability .01, we receive $0.
Which lottery do we prefer? Now consider the following
two lotteries:L3: With probability .11, we receive $1 million.
L2: With probability .89, we receive $0.
L4: With probability .10, we receive $5 million.
L2: With probability .90, we receive $0.
Which lottery do we prefer? Suppose (like most people), we
prefer L1 to L2. Show that L3 must have a larger expected
utility than L4.
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