nscarlisleh13

25.11.2019 • 

Mathematics

We will now derive the probability that a given observation is part of a bootstrap sample. suppose that we obtain a bootstrap sample from a set of n observations.

a. what is the probability that the first bootstrap observation is not the j^th observation from the original sample? justify your answer.

b. what is the probability that the second bootstrap observation is not the j^th observation from the original sample?

c. argue that the probability that the j^th observation is not in the bootstrap sample is (1 - 1/n)^n.

d. when n = 5, what is the probability that the j^th observation is in the bootstrap sample?

e. when n = 100, what is the probability that the j^th observation is in the bootstrap sample?

Ответ:

JessicaSontay8841

14.12.2022

Mathematics

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Step-by-step explanation:

We have sinA = 4/5 and sinB = 7/25.

=> cosA = sqrt(1 - sin²A) = 3/5

=> cosB = sqrt(1 - sin²B) = 24/25

P.S. Cosine must be positive in Quadrant I.

sin(A - B)

= sinAcosB - cosAsinB

= (4/5)(24/25) - (3/5)(7/25)

= 75/125 = 3/5. (Shown)

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