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Suppose that you
flip a fair coin (P(H)=P(T)=1
2 ) three times and you record if it landed on heads, H, or tails,
(a) What is the sample space of this experiment? What is the probability of each event?
(b) [1 pt] Let X be the number of times that you observe heads. What type of random variable is X?
(c) What is the probability distribution of X?

  • Needs probability and statistics help -

    By the way, it is not clear to me from the wording of the question if h, t, t is the same as t, h , t or not
    the first way there are 6 possible outcomes. The second way there are 8

    If order does not matter
    1 h h h
    2 h h t
    3 h t t
    4 t t t

    probability of each event here is 1/4

    if order does matter

    1 h h h
    2 h h t
    3 h t h
    4 h t t
    5 t t t
    6 t t h
    7 t h t
    8 t h h
    probability of each event here is 1/8

  • stor -

    In the second list, listing all possible outcomes there is one way to get three heads p(3h) = 1/8
    three ways of getting two heads
    p(2h) = 3/8
    three ways of getting 1 head
    p(1h) = 3/8
    one way of getting 0 heads
    p (0h) = 1/8

    let's look at a binomial distribution where p(h) = 1/2
    n = number of trials = 3
    k = number of successes (number of heads)
    p(h = k) = C(n,k) p^k (1-p)^k

    p(h=3) = c(3,3)(1/2)^3(1/2)^0
    = 3!/[3!*0!](1/8)(1) = 1/8

    p(h=1) = C(3,1)(1/2)(1/2)^2
    c(3,1) = 3!/[1!(3-1)!] = 3*2/2 = 3
    p(h=1) = 3(1/2)(1/4) = 3/8

    you will find that p(h=2) = C(3,2)((1/2)^2(1/2)^1 = 3/8

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