In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. The two parameters of the gamma distribution are alpha, a shape parameter, and beta, a scale parameter. In Excel, a random value can be simulated from a gamma distribution using GAMMA.INV(RAND(), alpha, beta). Consider a gamma distribution characterized by shape parameter alpha = 4 and scale parameter beta = 3. Estimate the 40th percentile of this distribution using Monte Carlo simulation. Use GAMMA.INV to randomly generate n = 2000 values of the distribution, then find the 40th percentile of the simulated gamma data values. Understanding that answers from simulations are subject to sampling variability, choose the answer choice that is closest to your simulated value. Hint: After completing this simulation problem, you should close the Excel file. Open Excel simulation spreadsheets involving the RAND() function can slow down your computer's performance as the RAND() function repeatedly re-evaluates.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.