Questions from Calculus

Q: The density function f (x) for the lifetime of a

The density function f (x) for the lifetime of a certain battery is shown in Fig. 1. Each battery lasts between 3 and 10 hours. (a) Sketch the graph of the corresponding cumulative distribution functi...

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√x/16, 0 ≤ x ≤ 4

Q: A newspaper publisher estimates that the proportion X of space devoted to

A newspaper publisher estimates that the proportion X of space devoted to advertising on a given day is a random variable with the beta probability density f (x) = 30x2(1 - x)2, 0 ≤ x ≤ 1. (a) Find t...

Q: Let X be the proportion of new restaurants in a given year

Let X be the proportion of new restaurants in a given year that make a profit during their first year of operation, and suppose that the density function for X is f (x) = 20x3(1 - x), 0 ≤ x ≤ 1. (a)...

Q: The useful life (in hundreds of hours) of a certain

The useful life (in hundreds of hours) of a certain machine component is a random variable X with the cumulative distribution function F (x) = 1/9 x2, 0 ≤ x ≤ 3. (a) Find E(X ), and give an interpreta...

Q: The time (in minutes) required to complete an assembly on

The time (in minutes) required to complete an assembly on a production line is a random variable X with the cumulative distribution function F (x) = 1/125 x3, 0 ≤ x ≤ 5. (a) Find E(X ) and give an int...

Q: The amount of time (in minutes) that a person spends

The amount of time (in minutes) that a person spends reading the editorial page of the newspaper is a random variable with the density function f (x) = 1/72 x, 0 ≤ x ≤ 12. Find the average time spent...

Q: At a certain bus stop the time between buses is a random

At a certain bus stop the time between buses is a random variable X with the density function f (x) = 6x(10 - x)/1000, 0 ≤ x ≤ 10. Find the average time between buses.

Q: When preparing a bid on a large construction project, a contractor

When preparing a bid on a large construction project, a contractor analyzes how long each phase of the construction will take. Suppose that the contractor estimates that the time required for the elec...

Q: The amount of milk (in thousands of gallons) that a

The amount of milk (in thousands of gallons) that a dairy sells each week is a random variable X with the density function f (x) = 4(x - 1)3, 1 ≤ x ≤ 2. (See Fi...