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Statistics II Question

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vince_24:
To all the smart students on this forum, I have a question that needs answering & you guys are my final hope

My question is with regards to variance calculations.

I am really confused as to when to square the co-efficient and when we do not in terms of variance calculations.

Some examples are set out below


* If we have X~Po(4) and Y~Po(6) - How do we calculate the variance of 2x+4y? Would it be 2^2Var(x) + 4^2Var(y) or 2Var(x) + 4Var(y)
* If we have a fair coin being tossed 5 times, If we want to calculate the variance after being doubled, would it be 2^2Var(x) or 2Var(X)?
Any help on this matter is greatly appreciated. I wish you all the best in your examinations.

astarmathsandphysics:
For a poisson the variance is the mean in this case 2 and 4 resp so var(2x+4y) =2*4+4*6

astarmathsandphysics:
I dont understand the second question. What is doubled? The variance for a binomial distribution is np(1-p) If the number of throws is doubled then the variance is doubled

vince_24:
It is from the May June 03 Paper.

A fair coin is tossed 5 times and the number of heads is recorded.

(i) The random variable X is the number of heads. State the mean and variance of X [Understand]
(ii) The number of heads is doubled and denoted by the random variable Y. State the mean and variance of Y. [Do Not Understand]

astarmathsandphysics:
The vaiance of y is orriginally 5*0.5(1-0.5) anf when y is doubled the new variance is 2^2*5*0.5(1-0.5)

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