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
Here is what i have worked out so far.
variance of x
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?
- BeeFreeLv 78 years agoFavorite Answer
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
- 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. :)