Suppose a coin is weighted so the probability of heads is really 0.6. Find the exact...

Suppose a coin is weighted so the probability of heads is really 0.6. Find the exact sampling distribution of the sample proportion of 3 flips of the coin that are heads.

Expert Solution

For a coin tossed the probability of head is 0.6. If a coin is tossed 3 times then the sampling distribution for 3 flips of coin is obtained by obtaining the probability of heads occuring at different times.

Let X be a random variable which denotes the number of heads. Then X = 0, 1, 2, 3 which represents zero head , one head, two head and three head respectively.

In this case we have different cases for three flips which are given below

There for calculatong the probability of the sampling distribution we obtain the probability using binomial distribution with probabilitty of succes 0.6 given by

Above both tables give the sampling distribution of heads for 3 flips

orchestra answered 1 year ago

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