Questions from Calculus


Q: For any positive constants k and A, verify that the function

For any positive constants k and A, verify that the function f (x) = kAk/xk+1, x ≥ A, is a density function. The associated cumulative distribution function F (x) is called a Pareto distribution. Comp...

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Q: For any positive integer n, the function fn(x)

For any positive integer n, the function fn(x) = cn x(n-2)/2 e-x/2, x ≥ 0, where cn is an appropriate constant, is called the chi-square density function with n degrees of freedom. Find c2 and c4 such...

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Q: Table 4 is the probability table for a random variable X.

Table 4 is the probability table for a random variable X. Find E(X ), Var(X ), and the standard deviation of X. Table 4:

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Q: Find E(X ), Var(X ), and the standard

Find E(X ), Var(X ), and the standard deviation of X, where X is the random variable whose probability table is given in Table 5. Table 5:

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Q: Compute the variances of the three random variables whose probability tables are

Compute the variances of the three random variables whose probability tables are given in Table 6. Relate the sizes of the variances to the spread of the values of the random variable. Table 6:

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Q: A certain gas station sells X thousand gallons of gas each week

A certain gas station sells X thousand gallons of gas each week. Suppose that the cumulative distribution function for X is F (x) = 1 – ¼ (2 - x)2, 0 ≤ x ≤ 2. (a) If the tank contains 1.6 thousand gal...

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Q: Compute the variances of the two random variables whose probability tables are

Compute the variances of the two random variables whose probability tables are given in Table 7. Relate the sizes of the variances to the spread of the values of the random variables. Table 7:

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Q: The number of accidents per week at a busy intersection was recorded

The number of accidents per week at a busy intersection was recorded for a year. There were 11 weeks with no accidents, 26 weeks with one accident, 13 weeks with two accidents, and 2 weeks with three...

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Q: The number of phone calls coming into a telephone switchboard during each

The number of phone calls coming into a telephone switchboard during each minute was recorded during an entire hour. During 30 of the 1-minute intervals there were no calls, during 20 intervals there...

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Q: Consider a circle with radius 1. (a) What

Consider a circle with radius 1. (a) What percentage of the points lies within ½ unit of the center? (b) Let c be a constant with 0 < c < 1. What percentage of the points lies within c unit of the cen...

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