A discrete random variable X can be described by the following probability funct

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A discrete random variable X can be described by the following probability function Calculate E[X]. Calculate Var(X). Graph the F(x), the cumulative probability function. What is P[X le 20]? Chapter 5, section 1, exercise 5 Suppose that an eddy current nondestructive evaluation technique for identifying cracks in critical metal parts has a probability of around 0.20 of detecting a single crack of length 0.003 in. in a certain material. Suppose further that n=8 specimens of this material, each containing a single crack of length 0.003 in., are inspected using this technique. Define a random variable, W = the # of these cracks that are detected. What is distribution of W? Calculate the following p[w = 3] P[W le 2] E [ W ] Var (W) the standard deviation of W Chapter 5, section 1, exercise 9 Transmission line interruptions in a telecommunications network occur at an average rate of one per day (i.e. 5 per five-day work week). a) What is the expected number of interruptions during the next five-day work week? Let X = the number of interruptions in the next five-day work week? 1. What is the appropriate distribution for X (with parameters)? Assess P [X = 0] Find EX and VarX Now consider the random variable Y = the number of weeks in the next four in which there are no interruptions What is a reasonable probability model for Y (just name it, don't specify parameters)? What are the values of the parameters for this model? (Hint: Use (b) from part a) Use this model to assess the probability that there will be two out of the four weeks with no interruptions.

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750 is too less for all the questions

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