... a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. = (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is (Round to three decimal places as needed.)

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Author:Amos Gilat
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For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random
variable x is within one standard deviation of the mean.
1
f(x) = x, [2,4]
.....
a) Find the mean.
(Round to three decimal places as needed.)
b) Find the standard deviation.
O =
(Round to three decimal places as needed.)
c) Find the probability that the random variable x is within one standard deviation of the mean.
The probability is
(Round to three decimal places as needed.)
Transcribed Image Text:For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. 1 f(x) = x, [2,4] ..... a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. O = (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is (Round to three decimal places as needed.)
Expert Solution
Step 1

Given that

X has following probability density function

f(x) = x/6, [2,4]

steps

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