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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?

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?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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Show full answers and steps deriving to the questions being asked in the exercise. Please don’t use R or excel when calculating expected value or variance. Formula calculate required
[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. 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. Plot the distribution of X. Does the distribution of X look like a normal distribution?
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