Questions from General Calculus

Q: Suppose you have just poured a cup of freshly brewed coffee with

Suppose you have just poured a cup of freshly brewed coffee with temperature 95°C in a room where the temperature is 20°C. (a) When do you think the coffee cools most quickly? What happens to the rate...

Q: Psychologists interested in learning theory study learning curves. A learning curve

Psychologists interested in learning theory study learning curves. A learning curve is the graph of a function P(t), the performance of someone learning a skill as a function of the training time t. T...

Q: Von Bertalanffy’s equation states that the rate of growth in length of

Von Bertalanffy’s equation states that the rate of growth in length of an individual fish is proportional to the difference between the current length L and the asymptotic length L` (in centimeters)....

Q: Let f(x) be the probability density function for the

Let f(x) be the probability density function for the lifetime of a manufacturer’s highest quality car tire, where x is measured in miles. Explain the meaning of each integral.

Q: Let f(t) be the probability density function for the

Let f(t) be the probability density function for the time it takes you to drive to school in the morning, where t is measured in minutes. Express the following probabilities as integrals. (a) The prob...

Q: Let f(x) = 30x2 (1 – x)

Let f(x) = 30x2 (1 – x)2 for 0 ≤ x ≤ 1 and f(x) − 0 for all other values of x. (a) Verify that f is a probability density fu...

Q: The density function / is an example of a logistic

The density function is an example of a logistic distribution. (a) Verify that f is a probability density function. (b) Find P(3 (c) Graph f. What does the mean appear to be? What about the median?

Q: Let f(x) = c/(1 = x2).

Let f(x) = c/(1 = x2). (a) For what value of c is f a probability density function? (b) For that value of c, find P(21 , X , 1).

Q: Let f(x) = k (3x – x2)

Let f(x) = k (3x – x2) if 0 ≤ x ≤ 3 and f(x) = 0 if x 3. (a) For what value of k is f a probability density function? (b) For that value of k, find P(X > 1). (c) Find the mean.

Q: A spinner from a board game randomly indicates a real number between

A spinner from a board game randomly indicates a real number between 0 and 10. The spinner is fair in the sense that it indicates a number in a given interval with the same probability as it indicates...