HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 233

Equations E1 and E2 These two equations can be used for calculations involving individual and cumulative Binomial probabilities. eg. Find the probability of at most 3 heads when tossing a coin 10 times. Ensure that formula E2 is ed and enter the values shown right. The value in J is irrelevant as it is merely the summation variable. Highlight V and press . Answer: 0.1719 Note: If N is larger than 200 then you should use a Normal approximation. The N!/((N-R)!*R!) section of the formula will cause internal overflow and inaccurate answers above this level. The time needed to perform the summation will probably also be excessive. Solve works by repeated iterations converging on the correct value and this will be quite slow if the summation has many terms. If it is important not to use a Normal approximation then replace the N!/((N-R)!*R!) portion with COMB(N,R). The COMB function has special facilities for handling large numbers. This will not help greatly with the iteration time needed. Equations E3 and E4 These two equations can be used for calculations involving individual and cumulative Poisson probabilities, where M is the mean. The technique is otherwise identical to the Binomial problem. Equation E5 The formula in E5 is a generic formula for problems such as the one below: "A probability distribution has the equation f (x) = 0.625x3 (2 − x) ; 0 ≤ x ≤ 2 . Show that this is a valid probability distribution function and use it to find P ( x ≤ 1.2) " Use it by substituting whatever function is in use for the one currently entered. As this formula involves the integration function, each use of the solve process will require the calculator to perform multiple integrations. Because of this the solving process will be relatively slow. 233