Multiplying a random variable by a constant

When a random variable is multiplied by a constant, the mean and standard deviation are multiplied by the same constant, and the variance is multiplied by the square of the constant: μ 3 X = μ X × 3 = 3 × 3 = 9.

1. How do you multiply random variables?
2. How does multiplying by a constant affect the variance?
3. What happens when you add a constant to a normal distribution?

How do you multiply random variables?

the product of two random variables is a random variable; addition and multiplication of random variables are both commutative; and. there is a notion of conjugation of random variables, satisfying (XY)^* = Y^*X^* and X^** = X for all random variables X,Y and coinciding with complex conjugation if X is a constant.

How does multiplying by a constant affect the variance?

Properties of the variance

If all the information is multiplied by a constant, the variance remains multiplied by the square of the constant.

What happens when you add a constant to a normal distribution?

Answer and Explanation: (i) If a constant is added to a normal distribution the result will be normal; Yes, this statement is true.