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.)

Question

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.)

BlackTom AI · Accepted Answer

To begin, restate the problem in my own words: we are told p = 0.3 and asked for the expected number of friend requests per day, with instructions to compute P(X = n) for n = 0, 1, 2, 3 and then use the expected value formula.

Assuming the number of trials (maximum possible friend requests per day) is n = 3, X follows a Binomial distribution with parameters n = 3 and p = 0.3. The probabilities are:
- P(X = 0) = (0.7)^3 = 0.343
- P(X = 1) = 3 × (0.3) × (0.7)^2 = 3 × 0.3 × 0.49 = 0.441
- P(X = 2) = 3 × (0.3)^2 × (0.7) = 3 × 0.09 × 0.7 = 0.189
- P(X = 3) = (0.3)^3 = 0.027

Next, apply the expected value formula for a Binomial distribution, E[X] = Σ x · P(X = x) over all x. Here:
E[X] = 0 × 0.343 + 1 × 0.441 + 2 × 0.189 + 3 × 0.027
      = 0.441 + 0.378 + 0.081
      = 0.900

Thus, the calculated expected number of friend requests per day, given n = 3 and p = 0.3, is 0.900. If one were to interpret the problem differently (for example, using a larger n so that the mean matches 1.800), the computed probability values and the resulting expectation would change accordingly. In the setup described here, the result derived from the n = 3 binomial model is 0.900.

Regarding the provided answer of 1.8000, note that doubling the mean would occur if the number of trials were increased (for instance, n = 6 would give E[X] = 6 × 0.3 = 1.8). Here, with n = 3, the mean is 0.9, which is consistent with the calculations above.

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.)数值题

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