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fatherbamboo
09.07.2019 •
Mathematics
8. based upon a long period of record keeping the following represents the probability distribution of the number of times the john jay wifi network is slow during a week. we call the random variable x. x 0 1 2 3 4 5 6 p(x) .08 .17 .21 k .21 k .13 a. what is the value of k? b. calculate the expected value of x. c. calculate the expected value of x^2 . d. calculate the variance of x. e. calculate the standard deviation of x f. calculate the variance of 3x. g. suppose that network slowness is independent from week to week. what is the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks? h. calculate the variance of the random variable x^2
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Ответ:
Part A:
The total value of p(x) = 1.
Thus,
.08 + .17 + .21 + k + .21 + k + .13 = 1
0.8 + 2k = 1
2k = 1 - 0.8 = 0.2
k = 0.2 / 2 = 0.1
Therefore, the value of k is 0.1
Part B:
The expected value of x is given by
Therefore, the expected value of x is 3.01
Part C:
The expected value of
Therefore, the expected value of
Part D:
The variance of x is given by
Therefore, the variance of x is 3.39.
Part E
The standard deviation of x is given by
Therefore, the standard deviation of x is 1.84.
Part F:
The variance of ax, where a is a constant is given by
Thus, the variance of 3x is given by
Therefore, the variance of 3x is 30.51.
Part G:
The probability that the network has no more that 4 slow times in one week is given by
Since, the network slowness is independent from week to week, the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks is given by
Therefore, the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks is 0.27
Part H:
The variance of x^2 is given by
Thus,
Therefore, the variance of the random variable
Ответ:
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