Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Random Variables - Distribution and Expectations

  1. Apr 4, 2012 #1
    Here is the homework question. I only have an issue with part c but have shown all my work up until then. Any help is appreciated!

    Mr and Mrs Brown decide to continue having children until they either have their first boy or until they have
    five children. Assume that each child is equally likely to be a boy or a girl, independent of all other children,
    and that there are no multiple births. Let B and G denote the numbers of boys and girls respectively that the
    Browns have.
    (a) Write down the sample space together with the probability of each sample point.
    Sample Space with probability = {B 1/2, GB 1/4, GGB 1/8, GGGB, 1/16, GGGGB 1/32, GGGGG 1/32}
    (b) Write down the distributions of the random variables B and G.
    Pr[B=0] = 1/32, Pr[B=1] = 31/32
    Pr[G=0] = 1/2, Pr[G=1] = 1/4, Pr[G=2] = 1/8, Pr[G=3] = 1/16, Pr[G=4] = 1/32, Pr[G=5] = 1/32,

    (c) Compute the expectations of B and G using a direct calculation
    E(B) = 31/32

    Is this below part correct. For some reason I don't think it could be correct.
    E(G) = 31/32??????
  2. jcsd
  3. Apr 4, 2012 #2


    User Avatar
    Science Advisor

    Hey topgun08 and welcome to the forums.

    Assuming your distribution for G is correct in part b, your answer is also correct. I used the calculation:

    E[G] = 0x1/2 + 1x1/4 + 2x1/8 + 3x1/16 + 4x1/32 + 5x1/32 = 0.96875 = 31/32
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook