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Problem. 19: Find the mean, variance, and standard deviation of the random variable X associated with the probability density function over the indicated interval. \(f(x) = \frac{5}{x^6} \); \(1 \le x < \infty\) (Round your answers to four decimal places if necessary.) mean ? variance ? standard deviation ? 

          Problem. 19: Find the mean, variance, and standard deviation of the random variable X associated with the probability density function over the indicated interval.
\(f(x) = \frac{5}{x^6} \); \(1 \le x < \infty\)
(Round your answers to four decimal places if necessary.)
mean
?
variance
?
standard deviation
?
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Problem. 19: Find the mean, variance, and standard deviation of the random variable X associated with the probability density function over the indicated interval. f(x) = (5)/(x^6); 1 ≤ x < ∞ (Round your answers to four decimal places if necessary.) mean ? variance ? standard deviation ?

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Problem 19: Find the mean, variance, and standard deviation of the random variable X associated with the probability density function over the indicated interval. f(x) = 5 / x^6; 1 <= x < ∞ (Round your answers to four decimal places if necessary.) standard deviation Problem 19: Find the mean, variance, and standard deviation of the random variable X associated with the probability density function over the indicated interval. f = 1 < 0 (Round your answers to four decimal places if necessary.) mean variance standard deviation
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Transcript

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00:01 For this question, we are given the probability distribution table here.
00:05 What do we have to find? we need to find the mean value.
00:08 Let's start with the mean value, which is also the expected value.
00:15 So the expected value and the mean is the same, which has the formula of the probability of x times the, i mean, x times the probability of x.
00:23 So the mean, which is equal to, which is denoted by x bar, by the way.
00:31 So this is the sum of, let me just write, this is negative 42 and multiply by 0 .36 and plus negative 27 times 0 .31 and plus negative 15 times.
00:46 This is 0 .24 and plus negative 6 times.
00:51 This is 0 .09.
00:53 Let's get the value here.
00:55 This is negative 42 times, which is 0 .36 and plus.
01:00 This is negative 27 times and 0 .31 and plus negative 15 times.
01:10 This is 0 .24 and plus.
01:16 Let me get this one here.
01:18 This is negative 27.
01:20 So this is plus negative 15 times, which is 0 .24 and plus.
01:21 Let me get this one here.
01:21 This is negative 27.
01:21 So this is plus negative 15 times, which is 0 .207.
01:26 And plus.
01:27 This is negative 6 and times .09.
01:32 So the value would be negative 207 .63...
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