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) = \\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.




Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS