Question

Let $X_1, X_2, \dots, X_n$ be IID random variables, where $X_i \sim \text{Uniform}(0, 1)$. Define the sample mean as $M_n = \frac{X_1 + X_2 + \dots + X_n}{n}$ Use Chebyshev's inequality to find an upper bound on $P\left[\left|M_n - \frac{1}{2}\right| \ge \frac{1}{100}\right] \le \frac{C}{n}$ Give the value of $C$ correct to the nearest integer.

          Let $X_1, X_2, \dots, X_n$ be IID random variables, where $X_i \sim \text{Uniform}(0, 1)$. Define the sample mean as

$M_n = \frac{X_1 + X_2 + \dots + X_n}{n}$

Use Chebyshev's inequality to find an upper bound on

$P\left[\left|M_n - \frac{1}{2}\right| \ge \frac{1}{100}\right] \le \frac{C}{n}$

Give the value of $C$ correct to the nearest integer.

Let X1, X2, …, Xn be IID random variables, where Xi ∼Uniform(0, 1). Define the sample mean as

Mn = (X1 + X2 + … + Xn)/(n)

Use Chebyshev's inequality to find an upper bound on

P[|Mn - (1)/(2)| ≥(1)/(100)] ≤(C)/(n)

Give the value of C correct to the nearest integer.

Added by Jamie R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Chai Santi

12/30/2021

Step 1

In this case, the mean is $\frac{0+1}{2} = \frac{1}{2}$. Show more…

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Let $X_1$, $X_2$, ..., $X_n$ be IID random variables, where $X_i$ ~ Uniform (0, 1). Define the sample mean as $M_n = \frac{X_1 + X_2 + ... + X_n}{n}$ Use Chebyshev's inequality to find an upper bound on $Pr[|M_n - \frac{1}{2}| \geq \frac{1}{100}] \leq \frac{C}{n}$ Give the value of C correct to the nearest integer.