Question
Download Solution PDFFor a random variable x having the PDF shown in the figure given below
the mean and variance are, respectively
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFUniform density function:
If the probability density function (pdf) is constant, the random variable is said to be uniformly distributed and the function is called ‘Uniform density function’
Calculation:
The general formula for the probability density function (pdf) for the uniform distribution is:
From the given pdf,
f(x) = ¼
Mean is calculated as:
E[X] =
Var[X] = E[X2] – {E[X]}2
E[X2] =
Var [X] = E[X2] - {E[X]}2
= 7/3 – (1)2
= 4/3
= 1.33
Direct Formula:
From the Uniform Density function we know two limits ‘a’ and ‘b’
Mean is defined as:
= 1
Variance is defined as:
= 1.33
Extra concept:
Statistical averages are defined below:
1. Mean or average value
2. Mean square value
3. Variance
4. Standard deviation
Last updated on Jul 2, 2025
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