# Complete 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.

Question

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.

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Step 1

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:

Step 2

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:

Step 3

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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