# Mathematical statistics and data analysis

Not what you're looking for?

Probability distribution and functions

##### Purchase this Solution

##### Solution Summary

The solution answers the question(s) below.

##### Solution Preview

1.)

a)

Frequency function for total number of attempts (say k): f(k)

STEP BY STEP:

probability that A will win in first attempt = p1

probability that B will win in 1st attempt = (1-p1)*p2

probability that A will win in 2nd attempt = (1-p1)*(1-p2)*p1

probability that B will win in 2nd attempt = (1-p1)^2*(1-p2)*p2

So on......

probability that A will win in nth attempt=((1-p1)*(1-p2))^(n-1)*p1

probability that B will win in nth attempt=(1-p1)^n*(1-p2)^(n-1)*p2

For total number of attempts = k

f k =2*n + 1 => A will win in it's (n+1)th attempt:

frequency function ( probability that the game will last for k atteamts):

f(k) = ((1-p1)*(1-p2))^n * p1 --Answer

if k =2*n => B will win in it's nth attempt:

f(k) = (1-p1)^n*(1-p2)^(n-1)*p2 --Answer

1.b) probability that player A will win:

p(A) = player A will win in it's 1st attempt OR in 2nd attempt OR 3rd attempt ..... so on

=> p(A) = p1 * (1-p1)*(1-p2)*p1 + ((1-p1)*(1-p2))^2*p1 + ((1-p1)*(1-p2))^3*p1 + ....

p(A) = p1/{1 - ((1-p1)*(1-p2))} --Answer

(Geometric series with 1st term p1 and common ratio (1-p1)*(1-p2))

2.) PLEASE LOOK AT YOUR PROBLEM AND JUST CHECK IF THERE IS ANY TYPO BECAUSE I'M NOT GETTING:

P(X>n+k-1 X>n-1) = P(X>k)

WHAT IS BETWEEN X>n+k-1 AND X>n-1 ?

Here, I'm giving you a brief intro of geometrical random variable.

because,

P(X= n) = q^(n-1) * p

( where p is the probability for event happening and ...

###### Education

- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India

###### Recent Feedback

- " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
- "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
- "Answer was correct"
- "Great thanks"
- "Perfect solution..thank you"

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

##### Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.