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Given the following
a. Compute the expected value for each distribution.
b. Compute the standard deviation for each distribution.
c. What is the probability that x will be at least 3 in Distribution A and Distribution B?
d. Compare the results of distributions A and B.
a.
Find the expected value for distribution A and distribution B.
Answer to Problem 1PS
The expected value of distribution A is 1, and distribution B is 3.
Explanation of Solution
Calculation:
The table of probability distributions for distribution A and B is given.
The formula for calculating expected value is
Here,
The expected value of distribution A is calculated by substituting the values in the above formula. It is calculated as,
The expected value of distribution B is
Thus, the expected value of distribution A and distribution B are 1 and 3, respectively.
b.
Find the standard deviation of distribution A and B.
Answer to Problem 1PS
The standard deviation for both distribution A and B is 1.22474.
Explanation of Solution
Calculation:
The standard deviation is calculated using the formula,
Here,
For distribution A,
For distribution B,
Thus, the standard deviation of distribution A and B is same, that is, 1.2247.
d.
Compare the results of the two distributions.
Answer to Problem 1PS
The mean value for distribution B is higher than distribution A but the standard deviation is same for both the distributions.
Explanation of Solution
From part a, the expected value for distribution A and B are obtained as 1 and 3, respectively. From part b, the standard deviation for both the distributions is obtained as 1.2247.
Thus, it can be said that the mean value or the expected value of distribution B is greater than that of distribution A. However, both of them have the same spread as the value of standard deviation is same.
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