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X and Y are independent random variables. The mean and variance of X are 2 and...

X and Y are independent random variables. The mean and variance of X are 2 and 1 respectively. The mean and variance of Y are 3 and 2 respectively. Which of the statements below about the random variable X-Y is true?

a. X-Y~Normal(-1,1)

b. X-Y~Normal(1,3)

c. X-Y has mean -1 and variance 3.

d. X-Y has mean 5 and variance 3.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

This question is based on the additive property of Normal distribution as sum or minus of Normal independent variates is also Normal distribution. Let X and Y are two random variables with mean and , and variance and respectively, therefore, X-Y will follow Normal with mean and variance , therefore in given question, X-Y will be normal with mean = 2-3 = -1, and variance = 1+2 = 3.

therefore option C is correct.

hii.. although I am trying to provide the detailed answer but if you have any doubt please ask by comment. your rating encourage us to provide the detailed and effective answers so please like the answer. thanks..

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