Questions from Calculus

Q: Find the value of k that makes the given function a probability

Find the value of k that makes the given function a probability density function on the specified interval. f (x) = kx, 1 ≤ x ≤ 3

Q: Find the value of k that makes the given function a probability

Find the value of k that makes the given function a probability density function on the specified interval. f (x) = kx2, 0 ≤ x ≤ 2

Q: Find the value of k that makes the given function a probability

Find the value of k that makes the given function a probability density function on the specified interval. f (x) = k, 5 ≤ x ≤ 20

Q: Find the value of k that makes the given function a probability

Find the value of k that makes the given function a probability density function on the specified interval. f (x) = k/√x, 1 ≤ x ≤ 4

Q: Verify that each of the following functions is a probability density function

Verify that each of the following functions is a probability density function. f (x) = 1/18 x, 0 ≤ x ≤ 6

Q: Find the expected value and variance for each random variable whose probability

Find the expected value and variance for each random variable whose probability density function is given. When computing the variance, use formula (5). f (x) = 1/4, 1 ≤ x ≤ 5

Q: Find the expected value and variance for each random variable whose probability

Find the expected value and variance for each random variable whose probability density function is given. When computing the variance, use formula (5). f (x) = 8/9 x, 0 ≤ x ≤ 32

Q: Find the expected value and variance for each random variable whose probability

Find the expected value and variance for each random variable whose probability density function is given. When computing the variance, use formula (5). f (x) = 5x4, 0 ≤ x ≤ 1

Q: Find the expected value and variance for each random variable whose probability

Find the expected value and variance for each random variable whose probability density function is given. When computing the variance, use formula (5). f (x) = 3/2 x – ¾ x2, 0 ≤ x ≤ 2

Q: Find the expected value and variance for each random variable whose probability

Find the expected value and variance for each random variable whose probability density function is given. When computing the variance, use formula (5). f (x) = 12 x(1 - x)2, 0 ≤ x ≤ 1