2. Suppose a magician has a weighted coin that comes up heads 40% of the time and tails 60% of the time. He tosses the coin 5 times. Define a random variable H to be the number of heads that appear in 5 tosses. a) Find the probability mass function (pmf) f for H and write the pmf in table form. b) Find P(H > 3) c) We have learned that the expected value of a random variable can be thought of as the mean value of the variable. The mode of a probability mass function f on a sample space S is an element x E S that maximizes f. Given this definition, find the mode of f where f is the pmf ofH.
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.
Given
P(Head) = 0.40
P(Tail) = 0.60
tosses 5 times
H= Number of heads that appear in 5 tosses of a coin
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