An unbiased coin is tossed 3 times. find the expected value of the number of heads and also its standard deviation
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Solution:-
Let 'x' denotes the number of heads which appear.
Then the possible values of x = 0, 1, 2,and 3
The corresponding possibilities = 1/8, 3/8, 3/8 and 1/8
So, the expected value of x is
= 0(1/8) + 1(3/8) + 2(3/8) + 3(1/8)
= 3/8 + 6/8 + 3/8
= 12/8
= 3/2
So, the expected value of number of heads is 3/2.
Now,
Standard Deviation (x) = √V(x)
= √3/2
= √1.5
Standard Deviation = 1.2247
Answer
Let 'x' denotes the number of heads which appear.
Then the possible values of x = 0, 1, 2,and 3
The corresponding possibilities = 1/8, 3/8, 3/8 and 1/8
So, the expected value of x is
= 0(1/8) + 1(3/8) + 2(3/8) + 3(1/8)
= 3/8 + 6/8 + 3/8
= 12/8
= 3/2
So, the expected value of number of heads is 3/2.
Now,
Standard Deviation (x) = √V(x)
= √3/2
= √1.5
Standard Deviation = 1.2247
Answer
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