Answer: 3 and 1.5
Step-by-step explanation:
In binomial distribution, the formula to find the mean and variance (respectively) is given by :-
![\mu=np\\ \sigma^2=np(1-p)](https://tex.z-dn.net/?f=%5Cmu%3Dnp%5C%5C%20%5Csigma%5E2%3Dnp%281-p%29)
, where n= Total number of trials.
p= probability of getting success in each trial.
Let X be the random variable that is the number of heads in the outcome.
Given : An experiment consists of tossing a coin 6 times.
i.e. n= 6
Also, total outcomes in coin =2 (tail , head)
Probability of getting head in each trial = (Favorable outcome)/ (Total outcome)
Mean = ![(6)(\dfrac{1}{2})=3](https://tex.z-dn.net/?f=%286%29%28%5Cdfrac%7B1%7D%7B2%7D%29%3D3)
Variance = ![\sigma^2=6(\dfrac{1}{2})(1-\dfrac{1}{2})](https://tex.z-dn.net/?f=%5Csigma%5E2%3D6%28%5Cdfrac%7B1%7D%7B2%7D%29%281-%5Cdfrac%7B1%7D%7B2%7D%29)
![=3(\dfrac{1}{2})=1.5](https://tex.z-dn.net/?f=%3D3%28%5Cdfrac%7B1%7D%7B2%7D%29%3D1.5)
Hence, the mean and variance of X is 3 and 1.5 respectively .