Question

let Y be a random variable with the mean , and standard deviation . Let W=2Y. compute the mean and standard deviation of W

Answer 1

Need help?

Answer 2

yyesss

Answer 3

What do you have so far?

Answer 4

um nothing. lol

Answer 5

i just know various equations:
sqare root of V(y)

Answer 6

E(y)=Sumation (P(y))

Answer 7

First, just curious: did they give you a specific value for E(Y) and
\[\sigma _{Y}\]

Answer 8

And, are you looking for an explanation or just the answer?

Answer 9

no . i was only given the info that i told u

Answer 10

preferably explanation with an answer

Answer 11

It might be more helpful if I give you the answers first.

E(W) = E(2Y) = 2*E(Y)

Stdv(W) = Stdv(2Y) = 2*Stdv(Y)

Answer 12

Think of it this way:

Let's say you have a random group of men whose average height is 6ft.

That's the same as saying their average height is 72 inches, right?

Well, that's just 12*E(Y) = E( 12*Y)

Does that part make sense? It's ok if it doesn't...

Answer 13

Sometimes you see it written as:

E(aX + b) = aE(X) + b
where "X" is your random variable and "a" and "b" are constants.

Answer 14

ya. it makes sense so far

Answer 15

i was thinking E(w/2)=Y

Answer 16

i really understand deviation and mean when using concrete examples. but what numbers do i plug in?

Answer 17

Well, I think the point is to rewrite the expected value of W in terms of the expected value of Y.
Also, don't just write "Y" -- you have to write "E(Y)" -- because Y is a random variable and, well, that's the kind of thing that teachers like to take points off for.

Last thing: Remember, the standard deviation is ALWAYS POSITIVE. So if you have
W = 2Y or W=-2Y, the standard deviation of W will be the same either way (i.e. it will equal 2*stdv(Y) ).

Answer 18

Here's an example: Try calculating the the mean and standard deviation of a roll of a die. Then, instead of 1,2,3,...,6 multiply each number by 5 and then recalculate the mean and standard deviation. i.e. with the same probabilities but the numbers 5,10,15, ..., 30

Answer 19

how do i do that?

Answer 20

5+10+15+20+25+30 / 6 ?

Answer 21

Yeah, you could. Or, if you happen to know that the expected value of a regular die throw is 3.5, then you can just multiply 5*3.5 = 17.5 and skip all that extra addition and division.

Answer 22

how do u know each is 3.5?

Answer 23

(1+2+3+4+5+6)/6

Answer 24

um okay? and that gives you the probability of each roll?

Answer 25

isnt each roll just 1/6 probable?

Answer 26

No, it gives the EXPECTED VALUE of each roll.

Answer 27

oh

Answer 28

okay so back to my example, how do i do it?

Answer 29

The probability is the same for all the sides

Answer 30

which example?

Answer 31

lol my very abstract question

Answer 32

the W=2Y?

Answer 33

what do i do with 2y=w?

Answer 34

yes

Answer 35

Oh yeah, ha! That one...

Answer 36

Go back to the dice roll. That's like me saying:

Roll a die. Take that number and multiply it by two. That's your random variable...

Answer 37

so its 2y^2?

Answer 38

E(2Y)=2y ^2 ?

Answer 39

No, just 2*Y

Answer 40

but you just said sqaure it?

Answer 41

When? I thought I said "multiply it by two"

Answer 42

ugh what do i do

Answer 43

If you have a random variable "Y" then since W=2Y, that means that the value of W is two times the value of Y.

Answer 44

okay so how do i find the mean ? and variance?