Answer 8 and 9 if possible **Exercise Problems and Solutions**---**Problem 7**Find the variance of \( X \) when \( X \) is \( \text{Exp}(\lambda) \).- Choices: - \(\frac{1}{\lambda}\) - \(\frac{2}{\lambda}\) - \(\frac{2}{\lambda^2}\) - \(\frac{1}{\lambda^2}\) - None of the above- Correct answer: N/A---**Problem 8**Find the variance of \( X \) when \( X \) is distributed as \( N(0, 1) \).- Choices: - 0 - -1 - 1 - 2 - -2- Correct answer: N/A---**Problem 9**Find \(\text{Std}(X)\) when \( X \) is a continuous random variable with the following given density:- Definitions: 1. \( f(x) = 2(1-x) \), on \([0,1]\), 2. \( f(x) = 0.01e^{-0.01x} \), on \([0, \infty)\), 3. \( f(x) = 3/x^4 \), on \([1, \infty)\), 4. \( f(x) = 2xe^{-x^2} \), on \([0,\infty)\), 5. \( f(x) = \frac{1}{2} \sin x \), on \((0, \pi)\).- Choices: - 1 - \(\frac{1}{18}\) - 18 - \( (18)^{-1/2} \) - None of the above- Correct answer: N/A---**Graph or Diagram Explanation:**There are no graphs or diagrams in the image. The document is a series of multiple choice questions (MCQs) designed to test knowledge on statistical distributions, specifically focusing on variance and standard deviation calculations.

Answered: Image /qna-images/answer/20833898-8b24-4627-a50c-a2dc3d78f43f.jpg

(8) Find the variance of X when X is distributed as N(0, 1). The correct answer is 2 N/A (Select One) (9) Find Std(X) when X is a continuous random variable with the following given density. (i) f(z) = 2(1 – z), on [0, 1], (iii) f(z) = 0.01e 0.01z on (0, 00), (v) f(z) = 3/z', on (1, 00), (vii) f(z) = 2ze², on [0, 00), (ix) f(x) = sin z, on (0, x), 1/18 (18)–1/2 1 18 None of the above N/A (i- Select One)