Discrete Probability Distribution

Question

Alice has noticed that the probability of any browsing customers eventually buying sth in the store is 18%, assume that the decisions of buying are independent of one another. Thus, what is the expected number of browsing customers who would buy sth in a group of 50 people ?

Answer 1

We note that $P(X_i=1) = 0.18$, where $X_i$ is an indicator that the customer $i$ buys smh, therefore $\mathbb E[X_i]=0.18$ for every $i$.

Therefore, We can write $S = \sum_{i=1}^{50} X_i$.

From the linearity of the expected value we get $\mathbb E[S] = \sum_{i=1}^{50} \mathbb E[X_i] = 50*\mathbb E[X_i] = 50*0.18 = 9 $.