Begin by creating a probability distribution for the number of heads in five tos

Question

Begin by creating a probability distribution for the number of heads in five tosses of a coin.

Explain why this distribution meets the conditions for a binomial distribution.

Use the discrete probability distribution to calculate the expected value of the random variable.

The expected value of the random variable is equal to the mean of the distribution. As mentioned in the list of properties of the binomial distribution, the mean of a binomial distribution is given by m = np. Use this formula to calculate the mean of this probability distribution.

Does the value you calculated in part b. match the value you calculated in part c.? Explain why or why not.

Explanation / Answer

a)

Binomial distribution is a discrete probability distribution. Tossing of coins five times gives a fixed number of observations n=5 and each of the observation would have a probability that event of interest has occured or not (i.e. we get heads or not) and also the probability of that remains the same (0.5 each time we toss a coin).

b)

c)

m=np

=5*0.5=2.5

In case b, we are calculating expected value of a cumulative discrete probability distribution whereas in part c we are calculating the mean of a binomial distribution and hence the value differs.

No of heads (x) P(x) x*P(x) 0 0.5 0 1 0.5 0.5 2 0.5 1 3 0.5 1.5 4 0.5 2 5 0.5 2.5 7.5

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