FRM Part I · FRM Exam Part I · Multivariate Random Variables
Discrete random variables X and Y have P(X=1)=0.40 and P(Y=1)=0.25. If X and Y are independent, what is P(X=1 or Y=1)?
The probability is 0.55. Under independence the joint probability is 0.40 times 0.25, which is 0.10. Adding the two marginals gives 0.65, and subtracting the double-counted overlap of 0.10 leaves 0.55.
- A0.65
- B0.55Correct
- C0.10
- D0.35
Explanation
Independence gives P(both)=0.40×0.25=0.10. P(X=1 or Y=1)=0.40+0.25−0.10=0.55. Option 0.65 ignores the overlap subtraction.
Did you get it right without looking?
One question tells you little. A timed set on Multivariate Random Variables shows your real accuracy, how long you take and where you lose marks.
More Multivariate Random Variables questions
- A multinomial experiment has three outcomes with probabilities 0.5, 0.3 and 0.2. In 10 independent trials, what is the probability of observ…
- X and Y are independent random variables with zero means and finite fourth moments. What is the standardized cokurtosis K(X,X,Y,Y) = E[X^2 Y…
- Binary variables X and Y are independent. P(X=1)=0.60 and the joint probability P(X=1, Y=1)=0.18. What is the joint probability P(X=0, Y=0)?
- Which statement about independence and correlation of two random variables X and Y is correct?
- Which statement about independence and correlation of two random variables is correct?
- For two asset returns X and Y, the standard deviations are σX = 2 and σY = 3. The central moments are E[(X-μX)^2(Y-μY)] = 12 and E[(X-μX)(Y-…