In some applications the distribution of a discrete rv $X$ resembles the Poisson distribution except that zero is not a possible value of $X$. For example, let $X=$ the number of tattoos that an individual wants removed when she or he arrives at a tattoo-removal facility. Suppose the pmf of $X$ is$$p(x)=k \frac{e^{-\theta} \theta^{\mathrm{r}}}{x} \quad x=1,2,3, \ldots$$a. Determine the value of $k$. Hint: The sum of all probabilities in the Poisson pmf is $1,$ and this pmf must also sum to $1 .$ b. If the mean value of X is 2.313035, what is the probabilitythat an individual wants at most 5 tattoosremoved?c. Determine the standard deviation of X when themean value is as given in (b).[Note: The article “An Exploratory Investigation ofIdentity Negotiation and Tattoo Removal” (Academyof Marketing Science Review, vol. 12, no. 6, 2008) gavea sample of 22 observations on the number of tattoospeople wanted removed; estimates of m and s calculatedfrom the data were 2.318182 and 1.249242, respectively.]
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.
In some applications the distribution of a discrete rv $X$ resembles the Poisson distribution except that zero is not a possible value of $X$. For example, let $X=$ the number of tattoos that an individual wants removed when she or he arrives at a tattoo-removal facility. Suppose the pmf of $X$ is
$$
p(x)=k \frac{e^{-\theta} \theta^{\mathrm{r}}}{x} \quad x=1,2,3, \ldots
$$
a. Determine the value of $k$. Hint: The sum of all probabilities in the Poisson pmf is $1,$ and this pmf must also sum to $1 .$
b. If the mean value of X is 2.313035, what is the probability
that an individual wants at most 5 tattoos
removed?
c. Determine the standard deviation of X when the
mean value is as given in (b).
[Note: The article “An Exploratory Investigation of
Identity Negotiation and Tattoo Removal” (Academy
of Marketing Science Review, vol. 12, no. 6, 2008) gave
a sample of 22 observations on the number of tattoos
people wanted removed; estimates of m and s calculated
from the data were 2.318182 and 1.249242, respectively.]
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