-Adding a constant to a random variable increases the expectation of the random variable by that constant
-Multiplying a random variable by a constant means that the expected value of that random variable is multiplied by the constant
-Adding a constant to a random variable does not change the variance of the random variable
-Multiplying a random variable by a constant multiplies the variance of the random variable by the square of that constant
Memorise these rules and you'll be able to answer exam questions. Do some googling if you want to see proof of these rules and really understand them. In your example, you have
It looks like our answer for the expectation doesn'td agree. Now I'm confused...
newguy123 wrote:Anyway, something else: you say that the it "makes sense" that the expectation and variance of a Poisson distribution are lambda, but as far as I know that's at least as complicated as the rules for the expectation and variance. You might want to look here for an explanation of why the expectation of a Poisson distribution is lambda:
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