Contents
What is the difference between a random variable?
A variable is a symbol that represents some quantity. A variable is useful in mathematics because you can prove something without assuming the value of a variable and hence make a general statement over a range of values for that variable. A random variable is a value that follows some probability distribution.
What does it mean to subtract two random variables?
Even when we subtract two random variables, we still add their variances; subtracting two variables increases the overall variability in the outcomes. We can find the standard deviation of the combined distributions by taking the square root of the combined variances.
How to calculate the distribution of two random variables?
Distribution of the difference of two normal random variables. MU−V(t) = E[et(U−V)] = E[etU]E[etV] = MU(t)MV(t) =(MU(t))2 =(eμt+1 2t2σ2)2 = e2μt+t2σ2 The last expression is the moment generating function for a random variable distributed normal with mean 2μ and variance 2σ2. Thus U−V ∼ N(2μ,2σ2). For the third line from the bottom,…
How to find the difference between two lognormal random variables?
The best I can do is to take the Taylor series of both and get that the difference is the sum of the difference between two normal r.v’s and two chi-squared r.v.’s in addition to the rest of the difference between the rest of the terms.
How to calculate the difference between two independent normal variables?
Let Y have a normal distribution with mean μ y, variance σ y 2, and standard deviation σ y. If X and Y are independent, then X − Y will follow a normal distribution with mean μ x − μ y, variance σ x 2 + σ y 2, and standard deviation σ x 2 + σ y 2. The idea is that, if the two random variables are normal, then their difference will also be normal.
Which is the variance of a random variable?
The variance of random variable y is the expected value of the squared difference between our random variable y and the mean of y, or the expected value of y, squared. And that’s the same thing as sigma squared of y.