3. Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value w of W.
Let, \(W\) be a random variable giving the number of heads minus the number of tails in three tosses of a coin
i.e., \(W=(\) Number heads \(-\) Number of tails) in throwing of a coin thrice
Here, the sample space
\(S=\{H H H, H H T, H T H, H T T, T T T, T T H, T H T, T H H\}\)
Here \(W=w\) with \(w=3,1,-1,-3\)
\(W=\left\{\begin{aligned} \text { 3, With HHH } \\ \text { 1, With HHT, HTH, THH } \\-1 \text { , With TTH, THT, HTT } \\ \text { -3, With TTT } \end{aligned}\right\}\)
Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin
Q7. (2096) Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. Assume that the coin is biased so that a tail is twice as likely to occur as a head.List the elements of the sample space for the three tosses of a coin and to each sample point assign a value w of a) Find the probability distribution (p.m.f) of the random variable w. b) Find the...
Let W be a random variable giving the number of heads minus the number of fails in three tosses of a coin Assuming that a head is one-sixth as likely to occur, find the probability distribution of the random variable W Complete the following probability distribution of W W 3 1 - 1 - 3 f(w) (Type integers or simplified fractions)
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Let X represent the number of heads subtracts the number of tails obtained when a coin is tossed 3 times, i.e., X = number of heads − number of tails. (a) Find the probability mass function of X (b) Given that X is at least 0, what is the probability that X is at least 2
A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, then K = 5. For k 1, 2, , K, let Xk be a continuous random variable that is uniform over the interval [0, 5]. The Xk are independent of one another and of the coin flips. LetX = Σ i Xo Find the...
Problem(13) (10 points) An unfair coin is tossed, and it is assumed that the chance of getting a head, H. is (Thus the chance of setting tail, T. is.) Consider a random experiment of throwing the coin 5 times. Let S denote the sample space (a) (2 point) Describe the elements in S. (b) (2 point) Let X be the random variable that corresponds to the number of the heads coming up in the four times of tons. What are...
3. (PMF – 8 points) Consider a sequence of independent trials of fair coin tossing. Let X denote a random variable that indicates the number of coin tosses you tried until you get heads for the first time and let y denote a random variable that indicates the number of coin tosses you tried until you get tails for the first time. For example, X = 1 and Y = 2 if you get heads on the first try and...
In a game called heads, a player tosses a coin three times. S/he wins N$300 if 3 heads occur, N$200 if 2 heads occur, and N$100 if 1 head occurs. On the other hand, S/he loses N$1500 if no head occurs. Let Y be a random variable denoting the player's gain (or loss). The coin is biased such that the probability of landing heads up is 2/3. a) Find the probability distribution of Y b) Hence, or otherwise, find the...