4. a random variable x has a mean of 10 and a standard deviation of 3. if 2 is added to each value of x, what will the new mean and standard deviation be?

Adding 2 to each value of the random variable makes a new random variable . Its mean would be

since expectation is linear, and the expected value of a constant is that constant. is the mean of , so the new mean would be

The variance of a random variable is

so the variance of would be

We already know , so simplifying above, we get

Standard deviation is the square root of variance, so .

so the standard deviation remains unchanged at 3.

NB: More generally, the variance of for is

but the variance of a constant is 0. In this case, , so we're left with , as expected.

the answer is 1/4

step-by-step explanation:

the answer is 8/21

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