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jimmy1
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A random variable X follows a certain distribution. Now say I multiply the random variable X by a constant a. Does the new random variable aX follow the same distribution as X?
jimmy1 said:A random variable X follows a certain distribution. Now say I multiply the random variable X by a constant a. Does the new random variable aX follow the same distribution as X?
mheena said:we know that if X is normally distributed, then so cX for any nonzero real number c.
also X + d is normally distributed, for any real number d.
can anyone please show me the proof?thanks
A constant times a random variable is a mathematical expression involving a fixed number and a variable that takes on different numerical values with a certain probability. The resulting value of the expression will also be a random variable.
In science, a constant times a random variable is often used to model real-world phenomena that involve random variation. It allows scientists to quantify the uncertainty or randomness in their data and make predictions based on probability.
The expected value of a constant times a random variable is equal to the constant multiplied by the expected value of the random variable. This can be calculated by multiplying each possible value of the random variable by its corresponding probability and summing them together.
Yes, a constant times a random variable can have a negative value. The resulting value of the expression will depend on the value of the random variable, which can take on both positive and negative values.
The difference between a constant times a random variable and a random variable times a constant is the order in which the constant and variable are multiplied. In terms of expected value, the two expressions will be equal. However, the resulting random variable may have different probability distributions, depending on the specific values of the constant and the random variable.