Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Independent Random Variables
Let X and Y be independent random variables with X ~ N(2, 4) and Y ~ N(-4, 9) where N(μ , σ2) denotes a normal distribution with mean μ and variance σ2. Given ϕ(1) = 0.8413, ϕ(2) = 0.9772 and ϕ(3) = 0.9987 where ϕ(⋅) is the cumulative distribution function of a standard normal random variable. Which of the following statements are true?
1
Var(2X + Y) = 17
2
P(|2X + Y| ≤ 15) = 0.9974
3
Cov(3X + 2Y, 3X - 2Y) = 0
4
2X - Y ∼ N (0, 25)