Determine the mean and variance of the random variable with the following probability mass function. f left-parenthesis x right-parenthesis equals left-parenthesis 5divided by 6right-parenthesis left-parenthesis 1 divided by 6right-parenthesis superscript x baseline comma x equals number 0 , 1 , 2 , . . hint: use the formula for the sum of the infinite series where . give exact answers in form of fraction.

560

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1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

step-by-step explanation: