Question: 9. Let X be the force applied to a randomly selected beam for 150 hours, and let Y take the value 1 or 0 depending

9. Let X be the force applied to a randomly selected beam for 150 hours, and let Y take the 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 probability 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|Xx)= (-0.8+0.04x)4 1+(-0.8+0.04x)4

(a) Tabulate the joint PMF of X and Y. Are X and Y independent?

(b) Find the average force applied to beams that fail (E(X|Y = 1)), and the average force applied to beams that do not fail (E(X|Y = 0)).

P(Y=1|Xx)= (-0.8+0.04x)4 1+(-0.8+0.04x)4

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