Asked Oct 1, 2019

A fair coin is tossed 3 times. Let the random variable X denote the total number of heads that appear squared plus 2. For example X(HHT) = 22 + 2 = 6.

Find E(X).


Expert Answer

Step 1

Consider a random variable X which represents the total number of heads that appear squared plus two when a coin is tossed 3 times.

Since the coin is tossed 3 times, total number of heads that appears can be 0 , 1 , 2 ,3

Therefore, X can take following values:


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(o2+2),( +2),(2 +2).(3 +2) 2,3,6,11

Step 2

The probabilities for different values of X can be calculated as:


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P(X 2)P(0 heads) 1 8 P(X 3) P(1 heads) 3 P(X 6)P(2 heads) 3 P(X 11) P(3 heads) 1

Step 3

The probability distributio...


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3 6 11 X 2 13 1 P(X x) 8 8 8.


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