An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of heads in each outcome. For example, if the outcome is hth, then =Rhth2. Suppose that the random variable X is defined in terms of R as follows: =X−2R1. The values of X are given in the table below. Outcome tth thh hht htt ttt hhh hth tht Value of X 1 3 3 1 −1 5 3 1 Calculate the values of the probability distribution function of X, i.e. the function pX. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X pXx
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.
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of heads in each outcome. For example, if the outcome is hth, then =Rhth2. Suppose that the random variable X is defined in terms of R as follows: =X−2R1. The values of X are given in the table below.
| Outcome |
tth
|
thh
|
hht
|
htt
|
ttt
|
hhh
|
hth
|
tht
|
|---|---|---|---|---|---|---|---|---|
| Value of
X
|
1
|
3
|
3
|
1
|
−1
|
5
|
3
|
1
|
Calculate the values of the
|
|
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