Question
II. Find the mean, variance and the standard deviation of the probability distribution of
the random variable X if
for
.
the random variable X if
Ask by Carter Robbins. in the Philippines
Jan 02,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Mean: 5.5
Variance: 8.25
Standard Deviation: ≈2.872
Variance: 8.25
Standard Deviation: ≈2.872
Solution

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The Deep Dive
To find the mean
, variance
, and standard deviation
of the random variable
, which is uniformly distributed from 1 to 10, we start with the mean:
Since each
Next, to calculate the variance:
First, we find
:
Now variance:
Finally, the standard deviation is:
So, the mean is
, the variance is
, and the standard deviation is approximately
.