[4F-13] Suppose that waiting time until the next claim is exponentially distributed with mean of 4 days. For last 2 days, there have been no claims. Calculate the probability that waiting time until the next claim will exceed 4 more days (6 days in total). (Round to 4 decimals)

The probability that waiting time until the next claim will exceed 4 more days i.e. P(X>6/X>2) = 0.3679

Step-by-step explanation:

From the given information:

Let consider X to be a random variable that follows an exponential distribution fo the waiting time.

Then; since the mean is distributed between 1 - 4 days

Thus:

The objective is to determine:

Recall that:

= 0.3678794412

To four decimal places; we have:

The probability that waiting time until the next claim will exceed 4 more days i.e. P(X>6/X>2) = 0.3679

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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step-by-step explanation: