1. Math
  2. Statistics And Probability
  3. 4 your engineering buddies have built a large trebuchet a...

Question: 4 your engineering buddies have built a large trebuchet a...

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4. Your engineering buddies have built a large trebuchet (a machine that can throw heavy objects, like a a catapult). They decide to launch 50 pounds of gravel at Donald Bren Hal Define X to be a random variable denoting how many windows will be broken by the fusillade of gravel. The probability mass function (pmf) of X is as follows: pounads of gravl t D 0 2345678910 P(X0.050.15 0.200.250.20 0.10 0.03 0.01.005.003 .002 (a) Verify that f(x) is a valid probability mass function (b) Find the probability that at least 4 windows will be broken. (c) Compute the expected number of windows that will be broken (the expectation X) (d) Compute the expected value of X2 e) Compute VAR[X] EX1- (ELX)

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