Question

5.26 Assume that the random variable Y is uniformly distributed over the interval $a \le Y \le b$. Verify the following: a. $\mu = \frac{a + b}{2}$ and $\sigma^2 = \frac{(b - a)^2}{12}$ b. $F(y) = \begin{cases} \frac{y - a}{b - a} & \text{if } a \le y \le b\\0 & \text{if } y < a\\1 & \text{if } y > b \end{cases}$

          5.26 Assume that the random variable Y is uniformly distributed over the interval $a \le Y \le b$. Verify the following:

a. $\mu = \frac{a + b}{2}$ and $\sigma^2 = \frac{(b - a)^2}{12}$

b. $F(y) = \begin{cases} \frac{y - a}{b - a} & \text{if } a \le y \le b\\0 & \text{if } y < a\\1 & \text{if } y > b \end{cases}$

5.26 Assume that the random variable Y is uniformly distributed over the interval a ≤ Y ≤ b. Verify the following:

a. μ = (a + b)/(2) and σ^2 = ((b - a)^2)/(12)

b. F(y) = (y - a)/(b - a) if a ≤ y ≤ b
0 if y < a
1 if y > b

Added by Sherry R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

09/18/2023

Step 1

Given that Y is uniformly distributed over the interval a<=Y<=b, the mean (μ) can be calculated as: μ = (a + b) / 2 Show more…

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5.26 Assume that the random variable Y is uniformly distributed over the interval a<=Y<=b. Verify the following: a. mu =(a+b)/(2) and sigma ^(2)=((b-a)^(2))/(12) b. F(y)={((y-a)/(b-a) if a<=y<=b),(0 if y>b):} b-a2 12 9+D a.u= and 2 n 9sAsnJ! b F(y) b. 0 if y< a if y > b