Wasps. M. Goodisman et al. studied patterns in queen and worker wasps and published their findings in the article “Mating and Reproduction in the Wasp Vespula germanica” (Behavioral Ecology and Sociobiology, Vol. 51, No. 6, pp. 497–502). The number of male mates of a queen wasp has a Poisson distribution with parameter λ = 2.7. Find the probability that the number, Y , of male mates of a queen wasp is a. exactly two. b. at most two. c. between one and three, inclusive. d. On average, how many male mates does a queen wasp have? e. Construct a table of probabilities for the random variable Y . Compute the probabilities until they are zero to three decimal places. f. Draw a histogram of the probabilities in part (e).
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.
Wasps. M. Goodisman et al. studied patterns in queen and worker wasps and published their findings in the article “Mating and Reproduction in the Wasp Vespula germanica” (Behavioral Ecology and Sociobiology, Vol. 51, No. 6, pp. 497–502). The number of male mates of a queen wasp has a Poisson distribution with parameter λ = 2.7. Find the probability that the number, Y , of male mates of a queen wasp is
a. exactly two.
b. at most two.
c. between one and three, inclusive.
d. On average, how many male mates does a queen wasp have?
e. Construct a table of probabilities for the random variable Y . Compute the probabilities until they are zero to three decimal places.
f. Draw a histogram of the probabilities in part (e).
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