5. Suppose there are 2 populations, each with mean ₁ and ₂ and standard deviation of ₁ and ₂ respectively. The interest is to measure a random variable X by taking a random sample of size n from the first population. In a similar manner, another random variable Y is measured by independently taking a random sample of size m from the second population. Assuming n and m are sufficiently large, then demonstrate the following properties: X~N (μ₁, 1) b. Y~N (μ₂, 1) a. c. (X-Ỹ)-N (1²₂-1 H₂, 11 + E

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