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Question: Compute the sampling distribution for two tosses of an unfair coin, where probability of a coin landing heads-up is 0.25; X = 1 represents for heads, and X = 0 represents for tails.



A ) Figure 1
B ) Figure 3
C ) Figure 4
D ) Figure 2

Steps to derive

1 The possible outcomes of tossing a coin 2 times are HH, HT, TH, TT.

2 The probability of getting a head is 0.25 and the probability of getting a tail is 0.75.

3 The probability of getting HH is (0.25)(0.25) = 0.0625

4 The sample mean for the outcome HH is 1+12 = 1
 [X = 1 corresponds to heads (H).]

5 Continue the same procedure to get the probabilities and sample means for all the outcomes.


6 The possible values of X are 0, 0.5 and 1. The desired sampling distribution is its probability distribution shown.




Hence the right answer is Option A

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