Questions from Applied Statistics

Q: The diameter of a particle of contamination (in micrometers) is

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f (x) = 2∕x3 for x > 1. Determine the following: a. P(X < 2) b. P(X > 5) c. P(4 < X < 8)...

Q: Suppose that f (x) = 0.5 cos x

Suppose that f (x) = 0.5 cos x for −π∕2 < x < π∕2. Determine the following: a. P(X < 0) b. P(X < −π∕4) c. P(−π∕4 < X < π∕4) d. P(X > −π∕4) e. x such that P(X < x) = 0.95

Q: Suppose that f (x) = x∕8 for 3

Suppose that f (x) = x∕8 for 3 < x < 5. Determine the following probabilities: a. P(X < 4) b. P(X > 3.5) c. P(4 < X < 5) d. P(X < 4.5) e. P(X < 3.5 or X > 4.5)

Q: Suppose that f (x) = 1.5x2 for −

Suppose that f (x) = 1.5x2 for −1 < x < 1. Determine the following: a. P(0 < X) b. P(0.5 < X) c. P(−0.5 ≤ X ≤ 0.5) d. P(X < −2) e. P(X < 0 or X > −0.5) f. x such that P(x < X) = 0.05.

Q: The probability density function of the net weight in pounds of a

The probability density function of the net weight in pounds of a packaged chemical herbicide is f (x) = 2.0 for 49.75 < x < 50.25 pounds. a. Determine the probability that a package weighs more than...

Q: Suppose that X is a random variable with probability distribution fX

Suppose that X is a random variable with probability distribution fX(x) = 1∕4, x = 1, 2, 3, 4 Determine the probability distribution of Y = 2X + 1.

Q: Suppose that X is a continuous random variable with probability distribution

Suppose that X is a continuous random variable with probability distribution fX(x) = x /18 , 0 ≤ x ≤ 6 a. Determine the probability distribution of the random variable Y = 2X + 10. b. Determine the ex...

Q: A random variable X has the probability distribution fX(x

A random variable X has the probability distribution fX(x) = e−x , x ≥ 0 Determine the probability distribution for the following: a. Y = X2 b. Y = X1/2 c. Y = ln X

Q: The velocity of a particle in a gas is a random variable

The velocity of a particle in a gas is a random variable V with probability distribution fV (v) = av2e−bv , v > 0 where b is a constant that depends on the temperature of the gas and the mass of the p...

Q: Suppose that X has the probability distribution fX(x)

Suppose that X has the probability distribution fX(x) = 1, 1 ≤ x ≤ 2 Determine the probability distribution of the random variable Y = eX.