Today (1/19/15) Learning objectives: propagation of moments with linear and nonlinear functions. Given y=(x) and a distribution in x with x and x, what are y and y? determining the pdf for linear and non-linear functions. Given y=(x) and a distribution in x according to the pdf f(x), what is g(y)? 2.0 : 1/11

Question 1 Consider ions passing through a pinhole and hitting a 1D detector as shown below. Given that the angular probability distribution of ions from the pinhole is given by f() = cos(), find the functional form of the pdf, g(y), measured at the linear strip detector. y L  where 0    /2 2.0 : 4/11

Question 2 Consider an MS experiment based on ion counting with a swept source (e.g., quadrupole). In a given sweep, a count is recorded every time one or more ions is detected in a given m/z channel, such that the measured counts will be binomially distributed. -Derive an expression to recover the mean number of ions µ in a single sweep from the measured probability of observing a count p. -What value of p corresponds to a mean bias of 1% from the true number of counts? 2.0 : 1/11

Thursday (1/21/15) Independent reading: 3.2 – Approximating nonlinear functions In-class lecture for 1/21/15: 3.1 – Sums of random variables 3.3 – Experimental standard deviation 2.0 : 1/11