--%>
Assignment Help - homework help

Probability on expected number of days

It doesn't rain often in Tucson. Yet, when it does, I want to be prepared. I have 2 umbrellas at home and 1 umbrella in my office. Before I leave my house, I check if it is raining. If it is, I take one of the umbrellas with me to work, where I would leave it. When I go back home, I check if it is raining. If it is, I take one of the umbrellas with me home; therefore, the number of umbrellas at my house and in my office changes with time. The probability of rain is 0.1 every time I leave either my office or my house. The event of rain is independent of location and what happened in the past. Find the expected number of days before I run out of umbrellas where I am and it is raining outside. Also find the probability that I am home when that happens.

E

Expert

Verified

The person has 2 umbrellas at home and 1 in office. Also the probability of raining is independent of other factors and is equal to 0.1.

Now let us find the probability distribution of
X: Number of days before he running out of umbrellas.

Now X can take values from 0,1,2,3,..

Let us find the probability X=0, Now since he have 2 umbrellas at home and one at office, this probability will be zero.

Now let us find the probability x=1, now here we are interested in finding the probability that he runs without umbrella on second day, this will happen in following manner.

When he will go office there is no rain, so probability is 0.9, now on returning there is rain with prob 0.1 now on second day leaving office there is no raining with 0.9 and at the time of return it rains with 0.1

Hence total probability is .9*.1*.9*.1

Now let us find the probability x=2, now here we are interested in finding the probability that he runs without umbrella on second day, this will happen in following manner.

This probability will be .1*.9*.1*.9*.1  (The probabilities are arranged according to event)
Now let us find the probability x=3, now here we are interested in finding the probability that he runs without umbrella on second day, this will happen in following manner.

The probability is .9*.1*.1*.1*.9*.1

The probability that more x ≥ 4 will be 1 minus all these probabilities

1053_probability.jpg

Hence the expected number of days is 3.97,

Means on an average more than 3 days required to run without umbrella.

   Related Questions in Advanced Statistics

  • Q : Bayesian Point Estimation What are the

    What are the Bayesian Point of estimation and what are the process of inference in Bayesian statistics?

    		•
  • Q : Analysing the Probabilities 1. In the

    1. In the waning seconds of Superbowl XLVII, the Baltimore Ravens elected to take a safety rather than punt the ball. A sports statistician wishes to analyze the effect this decision had on the probability of winning the game. (a) Which two of the following probabilities would most help t

    		•
  • Q : What is your statistical decision

    Question 1 Do parents with more children travel more than parents of small families? To find out, a survey was done of a large number of adults. Respondents were asked how many children they had and how many times

    		•
  • Q : Pearsons correlation coefficient The

    The table below illustrates the relationship between two variable X and Y. A

    		•
  • Q : Analytical Report Hi I WOULD LIKE TO

    Hi I WOULD LIKE TO KNOW IF YOU CAN HELP ME TO DO THE ASSIGNMENT IN HEALTH STATISTICS THANKS

    		•
  • Q : Random variables Random variables with

    Random variables with zero correlation are not necessarily independent. Give a simple example.    

    		•
  • Q : Problem related to playing cards Cards

    Cards are randomly drawn one at the time and with replacement from a standard deck of 52 playing cards. (a) Find the probability of getting the fourth spades on the 10th draw. (b) Determine the

    		•
  • Q : Probability of Rolling die problem A

    A fair die is rolled (independently) 12 times. (a) Let X denote the total number of 1’s in 12 rolls. Find the expected value and variance of X. (b) Determine the probability of obtaining e

    		•
  • Q : Statistics Homework with SAS File is

    File is attached, need it by 8:30 AM Pacific (Seattle, WA) time. No delay acceptable. Need it March 25, 2014 on 8:30 AM Pacific time.

    		•
  • Q : Error probability As of last year, only

    As of last year, only 20% of the employees in an organization used public transportation to commute to and from work. To determine if a recent campaign encouraging the use of public transportation has been effective, a random sample of 25 employees is to be interviewe

    		•