Let Tr be the number of fair coin tosses required to produce r heads, for r = 1, 2, . . . . Let Xn be the number of heads in n fair coin tosses. a) State the distribution of Xn (name and parameters). b) Find P (X5 ≤ 2). c) Find P(X365 ≤ 182). (Hint: no long calculations! There’s something special about the number 182.)
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.
Let Tr be the number of fair coin tosses required to produce r heads, for r = 1, 2, . . . .
Let Xn be the number of heads in n fair coin tosses.
a) State the distribution of Xn (name and parameters).
b) Find P (X5 ≤ 2).
c) Find P(X365 ≤ 182). (Hint: no long calculations! There’s something special about the number 182.)
d) State the distribution of Tr (name and parameters).
e) Show that P (Tr < 2r) = 1/2. (Hint: rewrite this
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a)
Let Xn be a random variable such that
Xn: The number of heads in n fair coin tosses.
Since the coin tossed is fair, p=0.5
Therefore, Xn follows Binomial Distribution with parameters n and 0.5.
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