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Thread: Simple probability

  1. #1
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    Simple probability

    Hello

    I am looking at a setup where I with probability $\displaystyle \frac{1}{4}$ get the outcome 2 otherwise the outcome is 6. I shall then formulate this mathematically and calculate the mean and variance.

    For the mean I calculate it like this:

    $\displaystyle \mu = \frac{1}{4} \cdot 2 + \frac{3}{4} \cdot 6 = 5$

    And rekcon that the variance will be given as:

    $\displaystyle \sigma = E\left[ X^2 \right] - \mu^2 = \left(\frac{1}{4} \cdot 2^2 + \frac{3}{4} \cdot 6^2 \right) - 5^2 =28 -25 =3 $

    For the mathematical formulation I am lost but are thinking something along a Binomial distribution, and does it make sense with the variance and mean?
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  2. #2
    MHF Contributor

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    Re: Simple probability

    The only "mathematical formulation" is P(2)= 1/4, P(6)= 3/4 with the set of outcomes being {2, 6}.

    (The "variance" is $\sigma^2= 3$, not $\sigma$. $\sigma$ is the 'standard deviation'. The variance is the square of the standard deviation.)
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