a) Two random variables are independent if their distribution is the product of

Question

a) Two random variables are independent if their distribution is the product of their marginal distributions. b) For a continuous random variable X, P(X = a) = 0 c) A discrete random variable will only have a finite number of possible outcomes. d) If rho = 0 for two random variables X and Y, then they are independent. Let X have a uniform distribution on the in (0, 10). Given that X = x, let Y have a uniform distribution on the interval (0, e^x). Find the joint marginal pdf of X and Y, and the pdf f_2(y). f(x, y) = f_2 (y) = {0

Explanation / Answer

True False.

1) True. This is a property of independent distributions such that P(AB)=P(A)*P(B)

2) True. For a continuous variable, we find the probability that x<a and not x=a.Probability of discrete value is 0.

3) True. A discrete random variable spread over a set an have only finite outcomes.

4) False. If correlation is zero, it is not necessary than the variables are independent. Example x and x^2 spread over the set (-1,0,1) have correlation of zero.

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