Its is probability and Statistics Class. I\'m extremely bad with these questions

Question

   Its is probability and Statistics Class. I'm extremely bad with these questions. If you could please write with pencil/pen with work STEP BY STEP, It would be awesome. Please think of it me as a challenged individual because I can't catch when steps are missed. Thank you so much.

Problem 8) (Note that a) and b) are separate problems) a) The probability that a computer running a certain operating system crashes on any given day is 0.1. Assume that the computer crashes are independent. What is the probability that the computer crashes for the first time on the tenth day after the operating system is installed. (6 points) (Round your answer to 4 decimal places) b) Let X denote a random variable that takes on any of the values-1, 0, 1 with respective probabilities P(X =-1) = 0.2 P(X 0) 0.5 P(X = 1) = 0.3 Compute E(X3) (6 points)

Explanation / Answer

a) Probability that the computer crashes on the 10th day the first time

= Probability that the computer does not crash on the first 9 days * Probability that the computer does crashes on the 10th day

= (1 - 0.1)9*0.1

= 0.0387

Therefore 0.0387 is the required probability here.

b) The required expected value here is computed as:

E(X2) = (-1)2P(X = -1) + 0 + 12P(X = 1) = 0.2 + 0 + 0.3 = 0.5

Therefore 0.5 is the expected value here.

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