Question

One fair coin is tossed 25 times, let X be the number of getting heads out of those 25 tossing experiments. What is the mean and variance of X?

12 and 6.25

10 and 2.5

12.5 and 6.25

12.5 and 2.5

Answer 1

The Given problem is solved using the Binomial distribution:

Binomial Distribution

If 'X' is the random variable representing the number of successes, the probability of getting ‘r’ successes and ‘n-r’ failures, in 'n' trails, ‘p’ probability of success ‘q’=(1-p) is given by the probability function

Then X follows Binomial distribution;

Mean of X = np

Variance of X =npq

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Success : Getting a Head

X: Number of getting heads out of 25 tossing experiments (Number of successes)

Number of experiments : Number of trails : n=25

Probability of getting a head when a fair coin is tossed (Probability of success) : p =1/2 =0.5

q=1-p=1-0.5=0.5

X follows Binomial distribution with n=25 and p=0.5

Therefore,

Mean of X = np =25 x 0.5 = 12.5

Variance of X = npq = 25 x 0.5 x 0.5 = 6.25

Ans :

12.5 and 6.25