Final answer:
To calculate the mean of a discrete probability distribution, multiply each outcome by its probability and sum the results. The mean of this distribution is 1.81. To calculate the standard deviation, calculate the variance first by multiplying the squared difference between each outcome and the mean by its probability, and then take the square root of the variance. The standard deviation in this case is approximately 0.876.
Step-by-step explanation:
To calculate the mean of a discrete probability distribution, you need to multiply each outcome by its corresponding probability and then sum up the results. In this case, you have four outcomes with their respective probabilities: 1 (0.18), 2 (0.25), 3 (0.35), and 4 (0.22). Multiply each outcome by its probability: 1 * 0.18 + 2 * 0.25 + 3 * 0.35 + 4 * 0.22 = 1.81. Therefore, the mean of this distribution is 1.81.
To calculate the standard deviation of a discrete probability distribution, you need to calculate the variance first. The variance is calculated by multiplying the squared difference between each outcome and the mean by its probability and summing up the results. In this case, the variance is calculated as follows: (1-1.81)^2 * 0.18 + (2-1.81)^2 * 0.25 + (3-1.81)^2 * 0.35 + (4-1.81)^2 * 0.22 = 0.7671. Finally, the standard deviation is the square root of the variance, which in this case is approximately 0.876.