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 required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

the answer would be c:   ax + b = ax + c

step-by-step explanation: