Answer: 3 and 1.5
Step-by-step explanation:
In binomial distribution, the formula to find the mean and variance (respectively) is given by :-
[tex]\mu=np\\ \sigma^2=np(1-p)[/tex]
, 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)
[tex]p=\dfrac{1}{2}[/tex]
Mean = [tex](6)(\dfrac{1}{2})=3[/tex]
Variance = [tex]\sigma^2=6(\dfrac{1}{2})(1-\dfrac{1}{2})[/tex]
[tex]=3(\dfrac{1}{2})=1.5[/tex]
Hence, the mean and variance of X is 3 and 1.5 respectively .
