The probability P(n) that an event characterized by a probability p occurs n times in N trials is given by the binomial distribution Consider a case where p << 1 and N >> 1.

Several approximations can then be made to reduce Eq. (1) to a simpler form. Using the result that In (1 - p) -p, show that (1 - p)^N_n e^-Np. Show that N!/(N A- n)! N^n. Use Stirling's approximation (Appendix A of Baierlein). Hence show that Eq. (1) reduces to W(n) lambda^n/n! e^-lambda where lambda = Np is the mean number of events.

The diagram represents the polynomial 4x2 + 23x – 72. what is the factored form of 4x2 + 23x – 72? (4x + 8)(x – 9) (4x – 8)(x + 9) (4x + 9)(x – 8) (4x – 9)(x + 8)

Desmond wants to sell his car that he paid $8,000 for 2 years ago. the car depreciated, or decreased in value, at a constant rate each month over a 2-year period. if x represents the monthly depreciation amount, which expression shows how much desmond can sell his car for today? 8,000 + 24x 8,000 - 24x 8,000 + 2x 8,000 - 2xdesmond wants to sell his car that he paid $8,000 for 2 years ago. the car depreciated, or decreased in value, at a constant rate each month over a 2-year period. if x represents the monthly depreciation amount, which expression shows how much desmond can sell his car for today? 8,000 + 24x 8,000 - 24x 8,000 + 2x 8,000 - 2x

What are the excluded values? m+5/mn+3m