Question
- Answer the following questions.
A random variable
has a mean 8 , a variance 9 , and an unknown probability
distribution. Using Chebyshev’s theorem, find the lower bound of
.
A random variable
distribution. Using Chebyshev’s theorem, find the lower bound of
Ask by West Warner. in Pakistan
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The lower bound of
is 0.25.
Solution

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The Deep Dive
Chebyshev’s theorem tells us that for any random variable, the proportion of observations that lie within
standard deviations of the mean is at least
. In this case, the mean
and the variance
, so the standard deviation
.
To find
, we consider
which is equivalent to
. Here, we define
as the number of standard deviations:
Now applying Chebyshev’s theorem:
Thus, the probability of being outside that range is:
So, the lower bound of
is at least
.