Thank you for visiting In video a game you are trying to shoot the targets Suppose that the number of the target is two The probobality of a succesful. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
a. Joint PMF Pxy(x,y)The random variables X and Y have the following values:If the first unsuccessful shot happens on the first shot, then we have X = 1, Y = 0.If the first unsuccessful shot happens on the second shot, then we have X = 2, Y = 1.If the first unsuccessful shot happens on the third shot, then we have X = 3, Y = 2.
If the first unsuccessful shot happens on the fourth shot, then we have X = 4, Y = 3.If the first unsuccessful shot happens on the fifth shot, then we have X = 5, Y = 4.The probability of a successful shot is 0.8, and the probability of an unsuccessful shot is 0.2.The probability of getting X = x and Y = y, where x = y and y is between 0 and x - 1, is given by:
P(X = x, Y = y)
= P(Y = y) P(X = x | Y = y)P(Y = y)
= [tex](0.2)^(y) * 0.8P(X = x | Y = y)
= (0.2)^(x - y - 1) * 0.8[/tex]
Therefore, we have:
P(1, 0) = 0.8P(2, 1)
= (0.2)(0.8)P(3, 2)
=[tex](0.2)^(2)(0.8)P(4, 3)[/tex]
= [tex](0.2)^(3)(0.8)P(5, 4)
= (0.2)^(4)(0.8)b.[/tex]
Marginal PMF Px(x) and Py(y)Px(x) is the probability that there were x targets shot before the first unsuccessful shot. This is equal to the probability that X = x. Therefore,
Px(1) = P(1, 0)
= 0.8Px(2)
= P(2, 1) + P(2, 0)
= (0.2)(0.8) + 0.8
= 0.96Px(3)
= P(3, 2) + P(3, 1) + P(3, 0)
= [tex](0.2)^(2)(0.8) + (0.2)(0.8) + 0.8[/tex]
= 0.992
Py(y) is the probability that there were y successful shots before the first unsuccessful shot. This is equal to the probability that Y = y. Therefore,
Py(0) = P(1, 0)
= 0.8Py(1)
= P(2, 1)
= (0.2)(0.8)
Py(2) = P(3, 2)
= [tex](0.2)^(2)(0.8)Py(3)[/tex]
= P(4, 3)
=[tex](0.2)^(3)(0.8)Py(4)[/tex]
= P(5, 4)
= [tex](0.2)^(4)(0.8)[/tex]
For more information on probability visit:
brainly.com/question/31828911
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