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[13] Suppose that X is a random variable that takes on the values 0, 1 and 2 with the following probabilities P[X = 0] = 0.3, P[X=1] = 0.20, P[X = 2] = 0.50 Suppose we take two independent draws from this distribution, denoted by X₁ and X2, and then compute the sample average X = (X₁ + X2) /2. a) Find E[X₁] and Var[X₁]. b) Find the sampling distribution of X (sample mean) for a sample size of 2. c) Plot the distribution of X. Does the distribution of X look like a normal distribution?

[13] Suppose that X is a random variable that takes on the values 0, 1 and 2 with the following probabilities P[X = 0] = 0.3, P[X=1] = 0.20, P[X = 2] = 0.50 Suppose we take two independent draws from this distribution, denoted by X₁ and X2, and then compute the sample average X = (X₁ + X2) /2. a) Find E[X₁] and Var[X₁]. b) Find the sampling distribution of X (sample mean) for a sample size of 2. c) Plot the distribution of X. Does the distribution of X look like a normal distribution?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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[13] Suppose that X is a random variable that takes on the values 0, 1 and 2 with the following probabilities P[X=0] = 0.3, P[X = 1] = 0.20, P[X = 2] = 0.50 Suppose we take two independent draws from this distribution, denoted by X₁ and X2, and then compute the sample average X = (X1 + X₂)/2. a) Find E[X₁] and Var[X₁]. b) Find the sampling distribution of X (sample mean) for a sample size of 2. c) Plot the distribution of X. Does the distribution of X look like a normal distribution?
Transcribed Image Text:[13] Suppose that X is a random variable that takes on the values 0, 1 and 2 with the following probabilities P[X=0] = 0.3, P[X = 1] = 0.20, P[X = 2] = 0.50 Suppose we take two independent draws from this distribution, denoted by X₁ and X2, and then compute the sample average X = (X1 + X₂)/2. a) Find E[X₁] and Var[X₁]. b) Find the sampling distribution of X (sample mean) for a sample size of 2. c) Plot the distribution of X. Does the distribution of X look like a normal distribution?
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