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: 0.677 0.203 0.079 0.023 0.013 0.005

​(a) Find the​ mean, variance, and standard deviation of the probability distribution. Find the mean of the probability distribution.

μ=

​(Round to one decimal place as​ needed.)

Answer 1

Concepts and reason

The probability is defined as the measure of the likelihood that an event will occur. The probability value is always lies between 0 and 1.

Probability distribution assigns a probability value to each of the possible value of a random variable.

Fundamentals

The formula for the calculating the expected value of x is,

$(s)=(x) $

The formula for the variance of the probability distribution is,

$v(x)={x?P(x)-[E(X)] $

The formula for the standard deviation of X is,

$o=JV(x) $

From the information, observe that following probability distribution.

The calculation of the mean is,

The calculation of the variance is,

The calculation of the required standard deviation is,

Ans:

The calculated value of the expected value for the given probability distribution is 0.507