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Social ScienceComplete parts (a) and (b) below.The number of dogs per household in a small townDogs012345Probability0.6160.2430.0920.0260.0140.009(a) Find the mean, variance, and standard deviation of the probability distribution.Find the mean of the probability distribution.
Complete parts (a) and (b) below.
The number of dogs per household in a small town
Dogs
0
1
2
3
4
5
Probability
0.616
0.243
0.092
0.026
0.014
0.009
(a) Find the mean, variance, and standard deviation of the probability distribution.
Find the mean of the probability distribution.
Expert Answer
a.
Find the average number of dogs per household in a small town using the given probability distribution.
Consider the variable X be the number of dogs per household in a small town.
The data represents the number of dogs per household in a small town and the corresponding probabilities of the number of dogs per household in a small town.
Mean:
The general formula to obtain the expected value or mean of a discrete random variable is,
µ = E(X) = ∑X*P(X)
The mean of the variable X is obtained as 0.606 from the calculation given below:
Obtain the variance of the variable X using the given probability distribution.
Variance:
The general formula to obtain the variance of a discrete random variable is,
V(X) = ∑X2*P(X) – (∑X*P(X))2
The variance of the variable X is obtained as 0.9268 from the calculation given below:
Obtain the standard deviation of the variable X using the given probability distribution.
Standard deviation:
The general formula to obtain the standard deviation of a discrete random variable is,
S.D (X) = SQRT(V(X)) = SQRT( ∑X2*P(X) – (&s...
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