dlee said:If X ~ N(2,4) then Y = -X-1 is also a normal random variable such that Y ~ N(μ,σ^2).
Find μ and σ^2.
I know that E(X) = 2 and Var(X) = 4.
E(Y) = -E(X) - 1
E(Y) = -2 - 1 = -3
So I found μ, but I'm not sure how to find the variance. Help?
In statistics, "N(μ,σ^2)" is a notation used to represent a normal distribution, where μ is the mean and σ^2 is the variance. Therefore, "X~N(2,4)" means that the random variable X follows a normal distribution with a mean of 2 and a variance of 4.
The mean of Y can be found by simply using the given value of μ, which is 2. In other words, μ = 2.
The variance of Y can be calculated using the formula σ^2 = E[(Y-μ)^2]. In this case, μ = 2 and we know that X~N(2,4), so we can substitute those values into the formula to find the variance of Y, which is σ^2 = 4.
A normal distribution is a type of probability distribution that is often used to represent real-world data. It is characterized by a bell-shaped curve, with the majority of the data falling within one standard deviation of the mean, and the remaining data spread out on either side. This type of distribution is common in many natural phenomena, such as human height or test scores.
Knowing the mean and variance of Y helps to describe the distribution of the data and make predictions about the likelihood of certain values occurring. For example, in this scenario, we know that most of the data will fall between 0 and 4, and the chances of a value being further from the mean decreases as the distance increases. It also allows for comparison to other datasets that may have a different mean and variance.