Finding x value, X is a normal random variable, mean, standard deviation, probability given HELP?

1. To determine the expected value of a R.V. given the density function, integrate the x*f(x) over the range defined by the density function. So, for this problem.

Integrate: x*(1/5)e^(-x/5) from 0 to infinity. It looks like you will have to do integration by parts, with f(x) = x and g'(x)=e^(-x/5). 2.

From #1, you have E(x). Remember, V(x)=E(x^2)-E(x)^2 So you now need to find E(x^2). E(x^2) is found the same way as above, except multiply f(x) by x^2 before you integrate instead of just x.

This problem will suck, because you will have to do integration by parts twice. Variance is easily found when you then have both components of the above equation. 3.

For number 3 above, you solve the same as #1. Except instead of multiplying f(x) by x and then integration over the defined range, you multiple by x+5 or (x+5)^2 - depending on whether you want (E(x+5))^2 or E((x+5)^2). Regardless, you will have to simplify your integral before attempting to integrate.

I'm guessing integration by parts will again be necessary. You also might should simplify the expected value expression. I.e.

E(x+5) = E(x) + E(5) = E(x)+5 Have Fun! If you don't have to show your work, find yourself a graphing calculator....

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