Consider X to be the number of heads obtained in 2 tosses of a fair coin. Suppos

Question

Consider X to be the number of heads obtained in 2 tosses of a fair coin. Suppose you are about to randomly choose 2 observations X1 and X2 from the population distribution (a) Determine the missing entries in the probability distribution table of X1 (give all answers to four decimal places) f(x) 0 .25 50 2 25 Total 1.00 (b) Determine the missing entries in the probability distribution table of X2 (give all answers to four decimal places) f(x) .25 .50 2 25 Total 1.00 (c) Since it is a random sample, X1 and X2 are independent (d)etermine the missing entries in the probability distribution table of X (give all answers to four decimal places) f(x) 0 0.5 1.5 Total 1.00 (e) Since it is a random sample, Cov(X1,X2)Select Submit Answer Save ress

Explanation / Answer

(d)

Following table shows the calculations:

So requried distribution is

X1 X2 bar(X) P(X1=x1) P(X1=x2) P(barx)=P(X1=x1)P(X2=x2) 0 0 0 0.25 0.25 0.0625 0 1 0.5 0.25 0.5 0.125 0 2 1 0.25 0.25 0.0625 1 0 0.5 0.5 0.25 0.125 1 1 1 0.5 0.5 0.25 1 2 1.5 0.5 0.25 0.125 2 0 1 0.25 0.25 0.0625 2 1 1.5 0.25 0.5 0.125 2 2 2 0.25 0.25 0.0625

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