SpaceX will launch a new rocket. Ten engineers that developed the rocket were asked what they...

 

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SpaceX will launch a new rocket. Ten engineers that developed the rocket were asked what they think the probability of successfully launching the rocket is. Here's the probability distribution for the probability of success (e) 0.6 0.7 0.8 proportion of votes 3/10 2/10 5/10 Consider that each launch of this new rocket has probability success equals . In other words, let X|0 = ~Bernoulli(0), where X = 1 if the rocket launch is successful and zero otherwise. Suppose that SpaceX will independently launch ten testing rockets before using the rocket in human mission. Assuming that X; and X;, ij, are conditionally independent given : a) Find the joint conditional pmf of X|0 = 0. b) Find the unconditional pmf of X = (X1,..., Xn). e) Find the pmf of O|X = x. d) Given that five out of the ten launches failed (i.e, X = 5), what is the probability that the probability of success for this new rocket (e) is equal to 0.8? Compare this probability with the initial (prior) probability of = 0.8. SpaceX will launch a new rocket. Ten engineers that developed the rocket were asked what they think the probability of successfully launching the rocket is. Here's the probability distribution for the probability of success (e) 0.6 0.7 0.8 proportion of votes 3/10 2/10 5/10 Consider that each launch of this new rocket has probability success equals . In other words, let X|0 = ~Bernoulli(0), where X = 1 if the rocket launch is successful and zero otherwise. Suppose that SpaceX will independently launch ten testing rockets before using the rocket in human mission. Assuming that X; and X;, ij, are conditionally independent given : a) Find the joint conditional pmf of X|0 = 0. b) Find the unconditional pmf of X = (X1,..., Xn). e) Find the pmf of O|X = x. d) Given that five out of the ten launches failed (i.e, X = 5), what is the probability that the probability of success for this new rocket (e) is equal to 0.8? Compare this probability with the initial (prior) probability of = 0.8.