Probability distributions are widely used in various fields such asstatistics, mathematics, physics, economics, and machine learning. The mean for the givenprobabilitydistribution is 17.The mean for a probability distribution can be calculated by multiplying each value of X by its corresponding probability P(X), and then summing up these products. In this case, the probability distribution is given as:X   P(X)10  0.620  0.230  0.140  0.1To calculate the mean, we multiply each value of X by its probability and sum up the results:(10 * 0.6) + (20 * 0.2) + (30 * 0.1) + (40 * 0.1) = 6 + 4 + 3 + 4 = 17.Therefore, themeanfor this probability distribution is 17.To further clarify, let's break down the calculation. Wemultiplyeach value of X by its probability:10 * 0.6 = 620 * 0.2 = 430 * 0.1 = 340 * 0.1 = 4Then, we sum up theseproductsto find the mean:6 + 4 + 3 + 4 = 17.The mean represents the average value in the distribution. In this case, it indicates that if we were to repeat this experiment many times, the average outcome would be 17. It provides a measure of central tendency for the probability distribution.Remember that the mean can be used as a summary statistic to describe the "typical" or "expected" value in a probability distribution. It is important to consider the context and interpret the mean in relation to the specific problem or situation at hand.In summary, the mean for the given probability distribution is 17.To know more aboutprobabilityvisit:brainly.com/question/33146788#SPJ11...

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