The expected value of the sample mean of the values obtained in these 300 tosses is 3.5
Given :
A fair six sided die is tossed 300 times
We have to find the expected value of the sample mean of the values obtained in these 300 tosses.
A dice have six sides:
In a fair dice every side has equal chance of occurrence,
Now the probability of presence of each side = 1/6
Now the expected value of the sample mean of the values obtained in these 300 tosses is given by:
E(x) = Σx P(x =x)
= 1*1/6 + 2*1/6 + 3*1/6 + 4*1/6 + 5*1/6 + 6*1/6
= 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6
= 1/6 (1+2+3+4+5+6)
= 1/6 (21)
= 21/6
E(x) = 3.5
Hence, the expected value of the sample mean of the values obtained in these 300 tosses is 3.5
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