Question

Let $W_{n}$ denote a random variable with mean $\mu$ and variance $b / n^{p}$, where $p>0, \mu$, and $b$ are constants (not functions of $n$ ). Prove that $W_{n}$ converges in probability to $\mu$. Hint: Use Chebyshev's inequality.

Name: Let Wn denote a random variable with mean μ and variance b / n^p, where p>0, μ, and b are constants (not functions of n ). Prove that Wn converges in probability to μ. Hint: Use Chebyshev's inequality.
Uploaded: 2022-10-06T07:42:03-08:00
Duration: 1 min 7 s
Channel: Sri K
Description: Let Wn denote a random variable with mean μ and variance b / n^p, where p>0, μ, and b are constants (not functions of n ). Prove that Wn converges in probability to μ. Hint: Use Chebyshev's inequality.

          Let $W_{n}$ denote a random variable with mean $\mu$ and variance $b / n^{p}$, where $p>0, \mu$, and $b$ are constants (not functions of $n$ ). Prove that $W_{n}$ converges in probability to $\mu$. Hint: Use Chebyshev's inequality.

Added by Alberto P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

10/06/2022

Step 1

More formally, we want to show that for any $\epsilon > 0$, the probability that $W_n$ is more than $\epsilon$ away from $\mu$ goes to zero as $n$ goes to infinity. This is the definition of convergence in probability. Show more…

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Let $W_{n}$ denote a random variable with mean $\mu$ and variance $b / n^{p}$, where $p>0, \mu$, and $b$ are constants (not functions of $n$ ). Prove that $W_{n}$ converges in probability to $\mu$. Hint: Use Chebyshev's inequality.