Question

5.6-6. A random sample of size $n = 25$ is taken from the distribution with pdf $f(x) = 2e^{-2x}$, $x > 0$. (a) Find $\mu$ and $\sigma^2$. (b) Find $P(0.20 \le \overline{X} \le 0.25)$, approximately.

          5.6-6. A random sample of size $n = 25$ is taken from the distribution with pdf $f(x) = 2e^{-2x}$, $x > 0$.
(a) Find $\mu$ and $\sigma^2$. (b) Find $P(0.20 \le \overline{X} \le 0.25)$, approximately.

5.6-6. A random sample of size n = 25 is taken from the distribution with pdf f(x) = 2e^-2x, x > 0.
(a) Find μ and σ^2. (b) Find P(0.20 ≤X≤ 0.25), approximately.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

05/18/2022

Step 1

The mean () of a random variable X with pdf f(x) = 2e^(-2x) is given by: = ∫x * f(x) dx from 0 to ∞ = ∫x * 2e^(-2x) dx from 0 to ∞ = 2 * ∫x * e^(-2x) dx from 0 to ∞ To find this integral, we can use integration by parts: Let u = x and dv = e^(-2x) dx Then, du Show more…

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5.6-6. A random sample of size n=25 is taken from the distribution with pdf f(x)=2e^(-2x),x>0. (a) Find mu and sigma ^(2). (b) Find P(0.20<=ar{x} <=0.25), approximately. Beed cimplete calculation formula 5.6-6. A random sample of size n = 25 is taken from the distribution with pdf f(x) = 2e-2x, x > 0. (a) Find and o2.(b) Find P(0.20 X 0.25) approximately.