Question

According to a study conducted by the Toronto-based social media analytics firm Sysomos, of all tweets get no reaction. That is, these are tweets that are not replied to or retweeted (Sysomos website, January ). Suppose we randomly select tweets.a. What is the expected number of these tweets with no reaction (to the nearest whole number)
a) What is the expected number of these tweets with no reaction?
b) What are the variance and standard deviation for the number of these tweets with no reaction?

Answer 1

Answer:

a) E(X) = 71

b) V(X) = 20.59

Sigma = 4.538

Step-by-step explanation:

The question is incomplete:

According to a 2010 study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction. That is, these are tweets that are not replied to or retweeted (Sysomos website, January 5, 2015).

Suppose we randomly select 100 tweets.

a) What is the expected number of these tweets with no reaction?

b) What are the variance and standard deviation for the number of these tweets with no reaction?

This can be modeled with the binomial distribution, with sample size n=100 and p=0.71, as the probability of no reaction for each individual tweet.

The expected number of these tweets with no reaction can be calcualted as the mean of the binomial random variable with these parameters:

$E(X)=n\cdot p=100\cdot 0.71=71$

The variance for the number of these tweets with no reaction can be calculated as the variance of the binomial distribution:

$V(X)=np(1-p)=100\cdot0.71\cdot0.29=20.59$

Then, the standard deviation becomes:

$\sigma=\sqrt{V(X}=\sqrt{20.59}=4.538$