Questions asked
Suppose \( X \) is a normal random variable with a mean of \( \mu \) and a variance of \( \sigma^{2} \). Calculate \( P(|x-\mu|<k \sigma) \) for \( k=1,2,3 \).
Suppose X is a normal random variable with a mean of µ and a variance of ?^2 Calculate P(|x ? µ| < k?) for k = 1, 2, 3.
5. Recall the pdf for a Gamma distribution with parameters \( \lambda \) and \( \alpha \) is \[ f_{X}(x)=\frac{\lambda^{\alpha}}{\Gamma(\alpha)} x^{\alpha-1} e^{-\lambda x}, \quad x>0 \] Suppose \( \alpha>2 \) and \( \lambda>0 \). Find \( E\left(\frac{1}{X}\right) \).
Aparna Shakti
Numerade educator
Urn 1 contains 2 white balls and 3 black balls. Urn 2 contains 4 white balls and 5 black balls. An urn is chosen at random, and then a ball is selected from that urn. What is the probability that the ball selected is white?
How many distinct solutions are there to x1 + x2 + x3 + x4 = 10 where each xi is taken from {0, 1, 2, . . . , 10}?
Find the directional derivative of f(x,y)=sin(x+2y) at the point (3, 4) in the direction ?=?/3. The gradient of f is: ?f(3,4)=? , ? The directional derivative is: