--%>
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 : MANOVA and Reflection Activity 10:

    Activity 10: MANOVA and Reflection 4Comparison of Multiple Outcome Variables This activity introduces you to a very common technique - MANOVA. MANOVA is simply an extension of an ANOVA and allows for the comparison of multiple outcome variables (again, a very common situation in research a

    		•
  • Q : Correlation Define the term Correlation

    Define the term Correlation and describe Correlation formula in brief.

    		•
  • 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 : Use the law of iterated expectation to

    Suppose we have a stick of length L. We break it once at some point X _

    Q : Statistics A nurse practitioner working

    A nurse practitioner working in a dermatology clinic is studying the efficacy of tretinoin in treating women’s post partum abdominal stretch marks. From a sample of 15 women, the mean reduction of stretch mark score is -0.33 with a sample standard deviation of 2.46. Describe what happens to the c

    		•
  • Q : Analyse the statistics of the data

    Assigment Question Select any two manufacturing companies and formulate the cost and revenue functions of the companies. analyse the statistics of the data and then sketch the functions and determine their breakeven points. (Note: You are required to interview the production and sales manag

    		•
  • 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 : How you would use randomization in

    The design of instrument controls affects how easily people can use them. An investigator used 25 students who were right-handed to determine whether right-handed subjects preferred right-handed threaded knobs. He had two machines that differed only in that one had a

    		•
  • Q : Non-parametric test what is the

    what is the appropriate non-parametric counterpart for the independent sample t test?

    		•
  • Q : Probability Distributions and Data

    1. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approxi

    		•