Let X be the force applied to a randomly selected beam for 150 hours, and let...

 

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Let X be the force applied to a randomly selected beam for 150 hours, and let Y take value 1 or 0 depending on whether the beam fails or not. The random variable X takes the values 4, 5, and 6 (in 100-lb units) with probabilities 0.3, 0.5, and 0.2, respectively. Suppose that the probability of failure when a force of X = x is applied is P(Y = 1|X = x) : (-0.8 + 0.04x)* 1+ (-0.8 + 0.04x)*' x = 4,5,6 a) Tabulate the joint pmf of X and Y. b) Are X and Y independent? c) Find the average force applied to beams that fail (i.e. E(X\Y = 1)), and the average force applied to beams that do not fail (i.e. E(X|Y = 0)). Let X be the force applied to a randomly selected beam for 150 hours, and let Y take value 1 or 0 depending on whether the beam fails or not. The random variable X takes the values 4, 5, and 6 (in 100-lb units) with probabilities 0.3, 0.5, and 0.2, respectively. Suppose that the probability of failure when a force of X = x is applied is P(Y = 1|X = x) : (-0.8 + 0.04x)* 1+ (-0.8 + 0.04x)*' x = 4,5,6 a) Tabulate the joint pmf of X and Y. b) Are X and Y independent? c) Find the average force applied to beams that fail (i.e. E(X\Y = 1)), and the average force applied to beams that do not fail (i.e. E(X|Y = 0)).

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