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Obtain the Probability Distribution of the Random Variable X\mathrm { X }

Question 97

Multiple Choice

Obtain the probability distribution of the random variable.
-When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT
Let X\mathrm { X } denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form.


A)
xP(X=x) 01/1611/823/831/841/16\begin{array}{r|r}x & P(X=x) \\\hline 0 & 1 / 16 \\1 & 1 / 8 \\2 & 3 / 8 \\3 & 1 / 8 \\4 & 1 / 16\end{array}

B)
xP(X=x) 01/1613/1621/233/1641/16\begin{array}{l|r}x & P(X=x) \\\hline 0 & 1 / 16 \\1 & 3 / 16 \\2 & 1 / 2 \\3 & 3 / 16 \\4 & 1 / 16\end{array}

C)
xP(X=x) 01/1611/423/831/441/16\begin{array}{r|r}x & P(X=x) \\\hline 0 & 1 / 16 \\1 & 1 / 4 \\2 & 3 / 8 \\3 & 1 / 4 \\4 & 1 / 16\end{array}

D)
xP(X=x) 11/427/1631/441/16\begin{array}{r|r}x & P(X=x) \\\hline 1 & 1 / 4 \\2 & 7 / 16 \\3 & 1 / 4 \\4 & 1 / 16\end{array}

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