Flip a fair coin four times and construct the sample space for all possible comb
ID: 3219243 • Letter: F
Question
Flip a fair coin four times and construct the sample space for all possible combinations.
a. Using the sample proportion of heads develop the sampling distribution for the sample space and calculate its expected values.
b. Compare the expectations to the population parameters. What conclusions can you draw about their relationship?
The prof asks us to do it in the statistics way not the math way, so i guess he means we gotta draw the graph and all that stuff. But if there is no way to draw graph and stuff then just do it the math way then.
Explanation / Answer
a. Using the sample proportion of heads develop the sampling distribution for the sample space and calculate its expected values.
The table of the sample space is given below:
The sample proportion of heads is
b. This part of the question is not appropriate because the expectations are derived from the population parameters under the assumption of fair coin. This is not obtained from samples to draw the conclusion differently. For instance, we start from the assumption of fair coin, list out the sample space, calculate the random variables, and expected values, and then comparing with population parameters is not appropriate at all.
b. Compare the expectations to the population parameters. What conclusions can you draw about their relationship?
toss1 toss2 toss3 toss4 H H H H T H H H H T H H T T H H H H T H T H T H H T T H T T T H H H H T T H H T H T H T T T H T H H T T T H T T H T T T T T T TRelated Questions
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