Let Y be a normal random variables, with mean 3 and variance 16.
Let V = (4-Y)/3
Find the variance of V
First, we need to find the mean of V:
E(V) = E[(4-Y)/3] = 4/3 - E(Y)/3 = 4/3 - 3/3 = 1/3
Next, we can use the formula for the variance of a linear transformation of a random variable:
Var(aX + b) = a^2Var(X)
In this case, a = 1/3 and b = 4/3, so:
Var(V) = Var[(4-Y)/3]
= (1/3)^2Var(Y)
= (1/9)(16)
= 16/9
Therefore, the variance of V is 16/9.
To find the variance of V, we can use the property of linear transformations of random variables.
First, let's find the expected value (mean) of V.
The expected value of V, denoted as E(V), is given by:
E(V) = E((4-Y)/3)
Since Y is a normal random variable with mean 3, we have:
E(V) = E((4-3)/3) = E(1/3) = 1/3
Next, let's find the variance of V.
The variance of V, denoted as Var(V), is given by:
Var(V) = Var((4-Y)/3)
Since Y is a normal random variable with variance 16, we have:
Var(V) = Var((4-3)/3) = Var(1/3) = (1/3)^2 * Var(1)
The variance of a constant is always 0. Therefore, Var(1) = 0.
Substituting this into the equation, we get:
Var(V) = (1/3)^2 * 0 = 0
Hence, the variance of V is 0.