What is the probability that the outcome of the first roll

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Reference no: EM132631378

Question 1) A fair coin with X = (head, tail) is tossed 3 times. What is the probability that at least one of the outcomes is tail?

Question 2) A six-sided fair die with X = (1, 2, 3, 4, 5, 6) is rolled twice. What is the probability that the outcome of the first roll is odd, or the outcome of the second roll is even?

Question 3) After Bob's yearly checkup, the doctor has bad news and good news for him. The bad news is that he tested positive for a serious disease, and the test's sensitivity and specificity are 90% and 80%, respectively. The good news is that this is a rare disease, striking only one in 5,000 people. What is the probability that Bob has the disease?

Question 4) Suppose that there are two e-commerce sites, A and B, for purchasing books. Site A receives 75% of all orders. Among the orders placed on site A, 80% arrive on time. Among the orders placed on site B, 60% arrive on time. Given that an
order arrived on time, find the probability that the order was placed on site B.

Question 5) Suppose you have a 4-sided die with X = (1, 2, 3, 4} where
A = Outcome of the rolling the die; and
p (A = 1) = 0.4, p (A = 2) = 0.2, p (A = 3) = 0.1, and p (A = 4) = 0.3
a. What is the mean (expected value) of A?
b. What is the variance of A?

Question 6) You are given a dataset with 5 data instances (i.e., N = 5), where the outputs are real valued (i.e., y_i ∈ R).

	x_i	y_i
i = 1	x_l	3.4
i = 2	x2	2.7
i = 3	x₃	4.3
i = 4	x4	3.7
i = 5	x_s	5.1

a. What is the mean (expected value) of the outputs?
b. What is the variance of the outputs?

Reference no: EM132631378

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