Children’s Gender. A certain couple is equally likely to have either a boy or a girl. If the family has four children, let X denote the number of girls. a. Identify the possible values of the random variable X. b. Determine the probability distribution of X. (Hint: There are 16 possible equally likely outcomes. One is GBBB, meaning the first born is a girl and the next three born are boys.) Use random-variable notation to represent each of the following events. Also use the special addition rule and the probability distribution obtained in part (b) to determine each event’s probability. The couple has c. exactly two girls. d. at least two girls. e. at most two girls. f. between one and three girls, inclusive. g. children all of the same gender.
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.
Children’s Gender. A certain couple is equally likely to have either a boy or a girl. If the family has four children, let X denote the number of girls.
a. Identify the possible values of the random variable X.
b. Determine the probability distribution of X. (Hint: There are 16 possible equally likely outcomes. One is GBBB, meaning the first born is a girl and the next three born are boys.)
Use random-variable notation to represent each of the following
c. exactly two girls.
d. at least two girls.
e. at most two girls.
f. between one and three girls, inclusive.
g. children all of the same gender.
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