Which of the following CANNOT be a probability distribution? Explain. i. p(x) = x / 6 for x = 1,2,3 ii. p x = x for x = 1,2,3 iii. p(x) = x / 5 for x = 1,0,1
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.
a. Which of the following CANNOT be a
i. p(x) = x / 6 for x = 1,2,3
ii. p x = x for x = 1,2,3
iii. p(x) = x / 5 for x = 1,0,1
b. An investor has $1000 available for a 1-year investment. The investor is
considering the following three options:
Option A
Possible return 30% 20% 0% -20%
Probability 25% 40% 20% 15%
Option B
Possible return 50% 30% 0% -40%
Probability 15% 50% 20% 15%
Option C
Guaranteed return 10%
Probability 100%
i. Based on the expected returns, which of these options should the
investor choose?
ii. Compute the standard deviations for Option A and Option B. Which
one of options A, B, and C has the least risk (i.e. the smallest standard
deviation), which one has the highest risk? What can you say about
the relationship between the expected returns and the risks of financial
assets in the normal situation?
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