Question

Suppose the random variable X has the uniform distirbution on [a,b]. Find expressions involving a and b for the expected valkue, variance, and standard deviation, of X. Check that your expressions when a=0 and b=10 addree with what you go in park c of part c of problem 5.

Answer 1

Answer:

Mean = 5

Variance = 8.3521

Standard Deviation = 2.89

Step-by-step explanation:

X has the uniform distribution on [a, b]

[a, b] = [a, 10]

Mean is solved using (a + b)/2

$= \frac{a + b}{2}\\= \frac{0 + 10}{2}\\= \frac{10}{2}\\= 5$

Standard Deviation = $\sqrt{variance}$

Standard Deviation =

$=\frac{b - a}{\sqrt{12} } \\= \frac{10 - 0}{\sqrt{12} } \\= \frac{10}{\sqrt{12} } \\= \frac{10}{3.464 } \\= 2.886836028\\ = 2.89$

Variance = $(Standard Deviation)^{2}$

Variance = $2.89^{2} = 8.3521$