Question

The Brann family wants to be financially prepared to have children. A financial advisor informs them that on the basis of families with similar characteristics, the probability distribution for the random variable X = number of children they might have is as follows:

No. of Children 0 1 2 3

Probability .05 .60 .30 .05

a. What is the expected value of X?

b. Explain what

Answer 1

a)
`E(X) =\sum_(i=1)^n X_i P(X_i) = 0*0.05+ 1*0.6 +2*0.3 + 3*0.5 =1.35`

b) For this case the expected value represent the most probably value for the distribution given.

So then the Brann family expect to have approximately 1.35 children based on the distribution given

c) No since we can't have 1.35 children, and the random variable is discrete but we can ensure that the expected value for the number of children would be between 1 and 2.

Explanation:

Previous concepts

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).

And the standard deviation of a random variable X is just the square root of the variance.

We have the following information given:

X 0 1 2 3

P(X) 0.05 0.6 0.3 0.05

With X="No. of Children"

Solution to the problem

Part a

The expected value can be calculated on this way:

`E(X) =\sum_(i=1)^n X_i P(X_i) = 0*0.05+ 1*0.6 +2*0.3 + 3*0.5 =1.35`

Part b: Explain what the expected value means in this situation

For this case the expected value represent the most probably value for the distribution given.

So then the Brann family expect to have approximately 1.35 children based on the distribution given

Part c: Is E(X) a possible outcome for th enumber of children that Brann familiy will have?

No since we can't have 1.35 children, and the random variable is discrete but we can ensure that the expected value for the number of children would be between 1 and 2.