6. This question is a simple exercise in changing variables. A gun fires at random in the angular range −π/2 < 0 < π/2 towards a wall a distance away. If y is the coordinate along the wall, show that 1 g(y)dy = 1 dy π 1 + (y/l)2 1 This, as we saw in the lectures, is the Cauchy distribution. Assuming that the mean should be zero from symmetry considerations, try to find the standard deviation; what problem do you have? Truncate the distribution at a distance |y| = L (not the same as 1) either side of the peak. Calculate the new normalisation constant, and find the standard deviation.

12.

12. Determine the equation of the normal to the tangent line at the point (2,1) for the function defined implicitly as: x2 + 4xy + y2 = 13

Given the table X = # of Red 0. 3 4. 0. 0. 6/252 12/252 3/252 12/252 54/252 36/252 3/252 3/252 36/252 54/252 12/252 3 3/252 12/252 6/252 what is P(Y=3)? Round your answer to 4 decimal places. Your answer 2)

2.3 pt 21