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Ann, a UBC student, receives "friend" requests on her Facebook account. For the past six months, the average number of such requests has been steady but the exact number of requests varies from day to day. After carefully collecting and observing data, she sees that the number of requests can be anywhere between 0 and 3. She notes that on 10% of the days she received 0 friend requests. The probability of receiving exactly 1 request is 0.3, and the probability for receiving exactly 2 requests is denoted by p. (The exact value of p may change from one question to another below.)

Flag question: Question 2

Let p = 0.25. Suppose we know that Ann received at least one friend request the other day. What is the probability that she received exactly 3 requests on that day?

(Hint: This is conditional probability. Recall: conditional probability = joint probability / marginal probability. Here, marginal probability is the probability of "at least one friend requests". And the joint probability refers to the event both "at least one friend" and "exact 3 friend requests". If the number of requests Ann receives is "at least one" AND "exactly 3", what should this number be?)

Flag question: Question 3

If p = 0.3, what is the expected number of friend requests per day?

(Hint: Compute the probability of P(X=n) for each n=0,1,2,3. Then apply the expected value formula.)

Flag question: Question 4

Suppose p = 0.1. Then, the expected number of friend requests can be shown to be 2 per day. What is the standard deviation of the number of friend requests per day?

Flag question: Question 5

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?)

Flag question: Question 6

For this problem, what is the most appropriate unit for the variance for the number of friend requests? (Select the best answer.)

Group of answer choices

-requests

-square root of requests

-requests squared

-none of the above

-no unit

-double requests