variance , mean of a random variable (JNU)

[Mauli]

 The random variable X has mean equal to 10 and variance equal to 9.
the random variable Y has a mean equal to 10 and a variance of 9.
Let Z = X/Y+3   , The mean of Z is
a) 3
b) 4
c) 22
d) None of these.

Please help someone!

[Amit Goyal]

This is an incomplete question. How are X and Y related? This information is crucial to answer this.

For example:
If Y  = X, then E(Z) = E(X/Y) + 3 = 4.
If Y is independent of X, then E(Z) = E(X/Y) + 3 = E(X)E(1/Y) + 3 = 10E(1/Y) + 3 = ? (the information given in the question is not sufficient to answer this)
and so on.

Mention the question number and the year in which this question was asked.

[Mauli]

Sir ,
this question has been asked in M.Phil/Ph.D in Economics in 2006 and 1993 or 1994 paper of M.A (JNU)

I am sorry , I do not have a soft copy of either of the papers but this is the question.

Q5.

[Amit Goyal]

Since the answer varies with the assumption on relation between X and Y, so, the best answer is None of the above.

[Mauli]

Thank you Sir :)