Question

Let \(X \sim N(\mu X, \sigma _X ^2)\) and \(Y \sim N(\mu _y, \sigma _y ^2)\) Which of the following is/are NOT correct?

• A. The area \(F(X)= \frac1{\sigma _x \sqrt{2\pi}}\)\(\int_{-\infty}^{\mu_x} e^{-\frac1{2}(\frac{X-\mu_x}{\sigma_x})^2} \)dx is 1.
• B. The areas under the normal probability curve between the ordinates at \(\mu_x ± 3\sigma_x\) , and \(\mu_y ± 3\sigma_y\) are 0.9544 and 0.9973, respectively.
• C. For variable X,
  Quartile Deviation: Mean Absolute Deviation: Standard Deviation ≅ \(\frac2{3} \sigma_x : \frac4{5}\sigma_x : \sigma_x\)
• D. If X and Y are independent, then \((X-Y) \sim N(\mu_x - \mu_y,  σ^2_x +σ^2_y)\).

Answer 1

The Correct Option is A, B

The correct option is (A): The area \(F(X)= \frac1{\sigma _x \sqrt{2\pi}}\)\(\int_{-\infty}^{\mu_x} e^{-\frac1{2}(\frac{X-\mu_x}{\sigma_x})^2} \)dx is 1. and (B): The areas under the normal probability curve between the ordinates at  \(\mu_x ± 3\sigma_x\) , and \(\mu_y ± 3\sigma_y\) are 0.9544 and 0.9973, respectively.