The number of coins that Jake spots when walking to work can be modeled as a...

The number of coins that Jake spots when walking to work can be modeled as a Poisson process with unit rate of 3/half an hour. Suppose it takes Jake half an hour each day to walk to work, and half an hour to walk back. Each coin is equally likely to be a penny, a nickel, a dime, or a quarter. Jake ignores the pennies but picks up the other coins.

(a) Find the expected amount of money that Jake picks up on his way to work. (b) Find the variance of the amount of money that Jake picks up on a given day. (c) Find the probability that Josh picks up exactly 5 cents on his way to work. You do not have to calculate this. Just provide an expression.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

The number of people arriving for treatment at an emergency room can be modeled by a...

The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of 5 per hour. In other words, the mean number of people arriving in one hour is 5. (Use R) (a) What is the probability that exactly four arrivals occur during a particular hour? (b) What is the probability that at least 4 people arrive during a particular hour? (c) What is the probability that at most 4...

The number of new businesses established in the US since 1990 can be modeled by the...

The number of new businesses established in the US since 1990 can be modeled by the function Nx=110.8x^3-5305.5x^2+76,701x+332,892 where x = 0 represents 1990 and the domain is [0, 25]. Use the First Derivative Test to determine the extrema of the function on the given domain. Classify as max/min and absolute/relative. For what intervals does the function increase/decrease? Please label and interpret each answer in the context of this problem.

The number of new businesses established in the US since 1990 can be modeled by the...

The number of new businesses established in the US since 1990 can be modeled by the function Nx=110.8x^3-5305.5x^2+76,701x+332,892 where x = 0 represents 1990 and the domain is [0, 25]. 6. Use the Second Derivative Test to discuss the concavity of this function on the given interval. What is the POI? Interpret the meaning of the POI in the context of this problem.

The number of new businesses established in the US since 1990 can be modeled by the...

The number of new businesses established in the US since 1990 can be modeled by the function Nx=110.8x^3-5305.5x^2+76,701x+332,892 where x = 0 represents 1990 and the domain is [0, 25]. 1) What was the average rate of change in the number of new businesses established between 2000 and 2010? Don’t forget to label and interpret the answers.

The number of new businesses established in the US since 1990 can be modeled by the...

The number of new businesses established in the US since 1990 can be modeled by the function Nx=110.8x^3-5305.5x^2+76,701x+332,892 where x = 0 represents 1990 and the domain is [0, 25]. According to the model, about how many new businesses were established in 2011? Don’t forget to label and interpret the answer. What was the average rate of change in the number of new businesses established between 2000 and 2010? Don’t forget to label and interpret the answers. What...

In his current job, Jake can work as many hours per day as he chooses and...

In his current job, Jake can work as many hours per day as he chooses and is paid $10 per hours. Faced with this wage schedule, he chooses to work 12 hours per day. A law has just been passed requiring employers to pay double wages for any hours in excess of 8 hours. True/False: Assuming that leisure is a normal good for Jake, he will certainly work more than 12 hours per day. With the use of an appropriate...

Let X be the random variable for the number of heads obtained when three fair coins...

Let X be the random variable for the number of heads obtained when three fair coins are tossed: (1) What is the probability function? (2) What is the mean? (3) What is the variance? (4) What is the mode?

How can V1 cells detect lines when photoreceptors detect only spots of light?

Consider a circular board game with 4 spots along its circumference. Each time, tosstwo fair coins....

Consider a circular board game with 4 spots along its circumference. Each time, tosstwo fair coins. For each Heads you obtain, move one spot clockwise. If you do not get any Heads, then move one spot counterclockwise. Repeat. a) Define your states to model this game a discrete-time Markov chain (DTMC). b) Verify that process {Xn, n = 0, 1, 2, ...} is a discrete-time Markov chain. Briefly discuss. c) Derive a transition probability matrix P. Briefly explain how you...

In a certain species of moth, there are two variations in the number of black spots...

In a certain species of moth, there are two variations in the number of black spots on the wings, either 2 or 4, which appear to be the result of a single gene. Scientists hypothesize that 4 spots is dominant to two spots. They cross two individuals that appear to be heterozygous for this trait and 140 offspring are produced. If 4 spots is in fact dominant: 1. how many would be expected to display 4 spots? 2. how many would...

Subjects