Suppose we do not know the exact value of p. However, we are given that the expected number of friend requests is 1.75, and the expected number of the square of friend requests is 3.95. What is the variance of the number of friend requests per day?

(Hint: Which formula for variance is helpful here?)

Question

Suppose we do not know the exact value of p. However, we are given that the expected number of friend requests is 1.75, and the expected number of the square of friend requests is 3.95. What is the variance of the number of friend requests per day?

(Hint: Which formula for variance is helpful here?)

BlackTom AI · Accepted Answer

We start by identifying the relevant statistics provided and the variance formula.
Given: E[X] = 1.75 and E[X^2] = 3.95, where X represents the number of friend requests per day.
The variance of a random variable X can be computed using the identity Var(X) = E[X^2] - (E[X])^2.
First, compute (E[X])^2: (1.75)^2 = 3.0625.
Next, subtract this from E[X^2]: 3.95 - 3.0625 = 0.8875.
Therefore, the variance Var(X) equals 0.8875.
This result aligns with the standard variance formula, which expresses variability in terms of the mean of the squares minus the square of the mean.
Since there are no alternative answer options provided in this case, there is no comparison to other choices to evaluate.

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