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    Probability distribution and functions

    © BrainMass Inc. brainmass.com November 29, 2021, 11:54 pm ad1c9bdddf
    https://brainmass.com/statistics/probability/mathematical-statistics-and-data-analysis-8877

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    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 ...

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