Question

A coin is tossed 4 times. Find the mean, variance, and standard deviation of the number of heads that will be obtained using the formulas of the binomial distribution.

Answer 1

The mean , variance and standard deviation will be 2 , 1 , and 1 respectively .

Binomial Distribution Moments :

Mean = np

Variance = npq

Standard Deviation  = $\sqrt{variance}$

where  n is the number of trials

           p is the probability of success in a single trial

 and    q , probability of failure in a single trial .

Probability of getting a head in a single trial = 1/2

                                                                     n = 4

Mean = np = 4*1/2

           = 2

Variance = npq = 4 * 1/2 * (1/2)

   = 1

Standard Deviation  = $\sqrt{variance}$ = $\sqrt{1}$ = 1

Therefore , mean = 2 , variance = 1 and standard deviation =1 .

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