Question

Let X be the number of heads obtained in 40 independent tosses of a fair coin Then X follows binomial distribution with parameters



​

Answer 1

Answer:

Explanation:

Suppose the head appears in x  

th

 toss. This means that tail appears in all preceding (x−1) tosses.

Now, if p is the probability of getting a head then probability of getting a tail is 1−p=q. So, the probability function of x will be f(x)=q  

x−1

p for x=1,2,3….. Now the expected of tosses will be

E(x)=ε  

x=1

∞

​  

xq  

x−1

p=  

q

p

​  

ε  

x=1

∞

​  

xq  

x

=  

q

p

​  

q(1+2q+3q  

2

+....)

=  

q

p

​  

q(1−q)  

−2

=  

pq

1

​  

.