Question

Probability and statistics for computer scientists answer page

Answer 1

The probability distribution represents the likelihood of different outcomes occurring in a random experiment. In this case, the probabilities for different numbers of pages featuring signature artists are calculated. The mean and standard deviation of the probability distribution are also calculated.

Step-by-step explanation:

The probability distribution represents the likelihood of each possible outcome occurring in a random experiment. In this case, the physics professor wants to know the probability of physics majors spending the next several years doing postgraduate research. The probability distribution provides the probabilities for different outcomes.

b.

1. The probability that two pages feature signature artists can be found by looking at the probability distribution and finding the corresponding probability. For example, if the probability of a page featuring a signature artist is 0.2, then the probability that two pages feature signature artists is:
2. P(X = 2) = (0.2)^2 * (1-0.2)^8 = 0.0016
3. To find the probability that at most six pages feature signature artists, you need to calculate the sum of probabilities for X = 0, 1, 2, 3, 4, 5, and 6.
4. P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
5. To find the probability that more than three pages feature signature artists, you need to calculate the sum of probabilities for X = 4, 5, 6, 7, 8, and 9.
6. P(X > 3) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)

c.

1. The mean, or expected value, is calculated by multiplying each possible outcome by its probability and summing the products. In this case, the mean can be calculated as:
2. Mean = 0 * 0.2 + 1 * 0.3 + 2 * 0.15 + 3 * 0.1 + 4 * 0.1 + 5 * 0.05 + 6 * 0.05 + 7 * 0.025 + 8 * 0.025 + 9 * 0.015 = 2.35
3. The standard deviation can be calculated using the formula:
4. Standard Deviation = sqrt[(0^2 * 0.2) + (1^2 * 0.3) + (2^2 * 0.15) + (3^2 * 0.1) + (4^2 * 0.1) + (5^2 * 0.05) + (6^2 * 0.05) + (7^2 * 0.025) + (8^2 * 0.025) + (9^2 * 0.015) - (mean^2)] = 2.09