Answer to Question #264351 in Statistics and Probability for ellie

Question #264351

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)

                                           


1
Expert's answer
2021-11-12T04:31:02-0500

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)=18P(X=0) = P(TTT) = \frac{1}{8}

P(X=1)=P(HTT,THT,TTH)=38P(X=1) = P(HTT,THT,TTH) = \frac{3}{8}

P(X=2)=P(HHT,HTH,THH)=38P(X=2) = P(HHT,HTH,THH) = \frac{3}{8}

P(X=3)=P(HHH)=18P(X=3) = P(HHH) = \frac{1}{8}

Following table shows the probability distribution of X:





ii. Find E(X)

E(X)=(0×18)+(1×38)+(2×38)+(3×18)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=1.5E(X)= 0+0.375+0.75+0.375=1.5


iii. Find Var(X)

Var(X)=ΣX2P(X)E(X)2Var(X)=\Sigma X^{2}P(X)-E(X)^{2}


Var(X)=3(1.5)2=0.75Var(X)=3-(1.5)^{2}=0.75


iv. Question is not given.




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