Questions from Calculus


Q: A small volume of blood is selected and examined under a microscope

A small volume of blood is selected and examined under a microscope, and the number of white blood cells is counted. Suppose that for healthy people the number of white blood cells in such a specimen...

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Q: A small volume of blood is selected and examined under a microscope

A small volume of blood is selected and examined under a microscope, and the number of white blood cells is counted. Suppose that for healthy people the number of white blood cells in such a specimen...

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Q: A small volume of blood is selected and examined under a microscope

A small volume of blood is selected and examined under a microscope, and the number of white blood cells is counted. Suppose that for healthy people the number of white blood cells in such a specimen...

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Q: A pair of dice is rolled until a 7 or an 11

A pair of dice is rolled until a 7 or an 11 appears, and the number of rolls preceding the final roll is observed. The probability of rolling 7 or 11 is 2/9. Determine the formula for pn, the probabil...

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Q: If the laboratory in Exercise 7 uses batches of 5 instead of

If the laboratory in Exercise 7 uses batches of 5 instead of 10 samples, the probability of a negative test on the mixture of 5 samples is (.95)5 = .774. Thus, Table 2 gives the probabilities for the...

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Q: A pair of dice is rolled until a 7 or an 11

A pair of dice is rolled until a 7 or an 11 appears, and the number of rolls preceding the final roll is observed. The probability of rolling 7 or 11 is 2/9. Determine the average number of consecutiv...

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Q: A pair of dice is rolled until a 7 or an 11

A pair of dice is rolled until a 7 or an 11 appears, and the number of rolls preceding the final roll is observed. The probability of rolling 7 or 11 is 2/9. What is the probability that at least thre...

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Q: Let X be a continuous random variable on 0 ≤ x ≤

Let X be a continuous random variable on 0 ≤ x ≤ 2, with the density function f (x) = 3/8 x2. (a) Calculate Pr (X ≤ 1) and Pr (1 ≤ X ≤ 1.5). (b) Find E(X ) and Var (X ).

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Q: Let X be a continuous random variable on 3 ≤ x ≤

Let X be a continuous random variable on 3 ≤ x ≤ 4, with the density function f (x) = 2(x - 3). (a) Calculate Pr (3.2 ≤ X ) and Pr (3 ≤ X ). (b) Find E(X ) and Var(X ).

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Q: For any number A, verify that f (x) =

For any number A, verify that f (x) = eA-x, x ≥ A, is a density function. Compute the associated cumulative distribution for X.

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