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# Calculate the expected value and variance of the random variable?

Calculate the expected value and variance of the random variable Y=10X + 5.

The probability distribution for random variable X is

x P(X=x)

2 0.07

5 0.23

8 0.34

11 0.36

Here is what i have worked out so far.

Forcast amount

2*0.07+5*0.23+8*0.34+11*0.36=7.97

variance of x

2^2(0.07)+5^2(0.23)+8^5(0.34)+11^2(0.36)= 71.35

Var(x)= 71.35-7.97^2 = 7.83

Any help would be much appreciated.

perfect, i had the same answer for the expected value! but am not quite sure how you have done the variance?

### 2 Answers

- BeeFreeLv 78 years agoFavorite Answer
mml -

Your formulas are perfect! I'm going to assume your math is correct ...

E(Y) = E(10X + 5) = 10(7.97) + 5 = 84.7

V(Y) = V(10X + 5) = 10^2 V(X) = 100(7.83) = 783

So, always ignore a constant term that is added or subtracted for the variance. BUT, a constant times a variance is always the constant squared.

Hope that helps

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- larryLv 43 years ago
there's a smart formula to get the variance V[x] = E[x^2] - E[x]^2 in words: variance of x is comparable to the envisioned fee of x minus the advise squared. having discovered the advise, you need to in common terms discover envisioned fee of x^2 and replace into the formula, you're able to do this the comparable way you discovered E[x] yet this time replace x with x^2. sturdy luck. :)

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