15. Homework: A body is emitting radiation with the following idealized spectrum of monochromatic flux density:...
Magnetic flux density is given as B =* = 6+ Problem [1] <15 points> on a surface given by r = 510,= = 48. Calculate the total flux o passing through this surface. For Problems 2 to 4: Figure shows a resistive loop with resistance of 2 Ohms. Magnetic flux density in this region is B = (2zł + 3xý)e ^. Calculate the current on this loop at t-0.1 seconds. 2 2 2 10 Problem [2] <10 points> Calculate the...
ºz hºz Problem [1] <15 points> Magnetic flux density is given as B = -2 on a surface given by r=5—10,0=5,2 = 48. Calculate the total flux o passing through this surface. r
Let X and Y have join density 6 f(x, y) =-(x + y)2, 0 < x < 1, 0 < y < 1
7. For the probability density function f(x) = for 0 <<<2 (a) Find P(x < 1) (b) Find the expected value. (c) Find the variance.
The probability density function of X is given by 0 elsewhere Find the probability density function of Y = X3 f(r)-(62(1-x)for0 < x < 1
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
. Consider the density funetion noiudue 0 < x < I fix)=k/x. elscwhere. 15. Consider the density funetion 2ib'svitslumo 0 1 fix)k. C. elscwhere. (a) Evaluate k (b) Find F(x) and use it to evaluate P(0.3 < X < 0.6) 15O bro nsy bhs nsom
Consider the probability density function 0 ifr <0 8.77 if 0 < x <1 0 if > 1 Find the median. Enter your answer to 3 decimal places. Answer:
2. (10 pts The random variables X and Y have joint density function f(x, y) == 22 + y2 <1. Compute the joint density function of R= x2 + y2 and = tan-1(Y/X).
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -