Recent content by HaLAA

  1. HaLAA

    Roll a fair die 5 times

    Yes, j,k,a,b gives the same outputs, we have 4 rolls have the same outputs.
  2. HaLAA

    Roll a fair die 5 times

    j,k,a,b are distinct indices, P (R_j,k and R_a,b) means j,k,a,bth rolls have the same outcomes
  3. HaLAA

    Roll a fair die 5 times

    Want to make sure i understand. The order of rolls doesn't matter. They are pairwise independent. However, not mutually independent be because P (R_j,k , R_a,b) is 1/6^3 and P (R_j,k) is 1/6 with district indices j,k,a,b
  4. HaLAA

    Roll a fair die 5 times

    If we let R_j,k be event that jth and kth rolls have the same outcome, then events R_j,k are't pairwise independent.
  5. HaLAA

    Roll a fair die 5 times

    I mean _ _ _... I _ _ _..._ j _ _ _...._ _k... something like this.
  6. HaLAA

    Roll a fair die 5 times

    Now , suppose we roll a die n times, would the probability that any ith, jth, kth, lth roll have the same outcomes still 1/6?
  7. HaLAA

    Roll a fair die 5 times

    I see that already, we have 6/36* 6^3/6^3=1/6
  8. HaLAA

    Roll a fair die 5 times

    I can have a combination of any 3 number of 6 if I understand correctly
  9. HaLAA

    Roll a fair die 5 times

    I don't understand your second question. The probability of two rolls of a die are the same is 1/6
  10. HaLAA

    Roll a fair die 5 times

    Homework Statement Roll a fair die 5 times, find the probability that the first two rolls have the same outcomes. Homework Equations The Attempt at a Solution The total outcomes is 6^5, I think we have 6^2 * 6 choose 2 /6^5 since the first two numbers are fixed and we can choose 2 numbers...
  11. HaLAA

    Expected value and variance of max{Y_1,Y_2}

    For x from 1 to 2, (x-1)^2 For x below 1, it is 0 For x greater than 2, it is 1
  12. HaLAA

    Expected value and variance of max{Y_1,Y_2}

    Homework Statement Let Y_1,Y_2 be independent random variable with uniform distribution on the interval [1,2]. Define X=max{Y_1,Y_2}. Find p.d.f., expected value and variance. Homework Equations The Attempt at a Solution Since $X=\max\{Y_1,Y_2\}$, this tells $Y_1$ and $Y_2$ must at most $x$...
  13. HaLAA

    Conditional Probability and law of total probability

    I never learn how to draw a tree
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