In the last graph work done between 1st point and last point is independent from path. Depends only on position of intial and final position. So this force is conservative.
• Problem 7. For a wave-function W.(x) = (2/a)" sin(x/a) calculate the average position (<x>). Is the function W.(x) = (2/a) sin(x/a) an eigenfunction of the x operator?
If X and Y have a joint probability density function specified by 2-(+2y) find P(X <Y).
(1 point) If X is a random variable with moment generating function ui) = (1-1)-9, t < I/7 then E(X) = and Var(X) =
The density function of X is given by + br if 0 r < 1 f(x) = 0 1 otherwise If E(X) = 3, find a and b. (Hint: Both values are integer.) a = b =
function Ckek osrs4 be a density 4. Let f(x)=3 otherwise Find: i) k = 24] P(-2<x<2)
7, Let X be a continuous random variable with probability density function: 0, f x<0 150 f x> 10 ind ihe avnanted value and mode of random variable X
2.6.17. The probability density function of the random variable X is given by 6x-21-3 -, 2<x<3 0, otherwise. Find the expected value of the random variable X.
QUESTION 28 Using the Binomial Probability table, find Px) when n - 7, X <3, and p 0.5 A, 0.273 O B. 0.500 O C. 0.227 ○ D. 0,773
7. Show that if the joint probability density function of X and Y is if 0 < x <.. =sin(x + y) f(x, y) = { VI fres 9 Line + »» Hosszž, osys elsewhere, then there exists no linear relation between X and Y.
3. (a) Explain why the function f(x) = {*** *8 sin (1) :051 <10 :3€ (-0, 0) (10,00) is a probability density function. That is, show or explain why f(x) satisfies all of the properties of a probability density function.