Statistics with Probability

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    Ezra Halleck

    A 6 sided dice is rolled 1000 times. Let be random variable which consists of 1 if a roll is 1 and 0 otherwise. Let X be the random variable which counts the number of 1’s in the 1000 rolls.
    a) Find expectation for and X and interpret.
    b) Find standard deviation for and X and interpret.


    See attachment for solution



    I found out another way to do standard deviation is the square root of n * p * q with q=1-p. This was helpful for the standard deviation of E[x] since it was harder to find than E[Xi]



    you can also get the variance of Xi by doing Var(Xi)= p(1-p) which is
    1/6(1-(1/6))= (1/6)(5/6) then that gives you 5/36 and when you take the square root of that to find the Sd you get .37
    easy and straight to the point



    ok thats useful


    It’s 3 in the morning…this is dreadful. Here, I believe this is more straight forward.



    for the last part: V[X} you forgot to multiply by 1000 so it’s going to be
    1000* 1/6 * 5/6 = 138.8889
    SD+ sqrt(138.889) = 11.78


    No, you don’t multiply. Divide. Pretty certain about that.

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