Three fair coins are tossed. Let X represent the number of tails.
i. Find the probability distribution of X. (3 marks)
ii. Find E(X). Show that this is equivalent to . (2 marks)
iii. Find Var(X). Show that this is equivalent to . (3 marks)
iv. Find . (2 marks)
i. Probability distribution of X
X = number of tails
If three coins are tossed then following events will occur:
S = [HHT, HTH, HHH, THH, HTT, TTH, THT, TTT]
Total no. of outcomes =23= 8
"P(X=0) = P(TTT) = \\frac{1}{8}"
"P(X=1) = P(HTT,THT,TTH) = \\frac{3}{8}"
"P(X=2) = P(HHT,HTH,THH) = \\frac{3}{8}"
"P(X=3) = P(HHH) = \\frac{1}{8}"
Following table shows the probability distribution of X:
ii. Find E(X)
"E(X) = (0\\times\\frac{1}{8})+(1\\times\\frac{3}{8})+(2\\times\\frac{3}{8})+(3\\times\\frac{1}{8})"
"E(X)= 0+0.375+0.75+0.375=1.5"
iii. Find Var(X)
"Var(X)=\\Sigma X^{2}P(X)-E(X)^{2}"
"Var(X)=3-(1.5)^{2}=0.75"
iv. Question is not given.
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