Question

Suppose that X is a binomial random variable with parameters n=20 and p=0.7.

Choose a wrong statement about the random variable X.

	a.	The maximum possible value of X is 20.
	b.	The minimum possible value of X is 0.
	c.	The variance of X is 4.2.
	d.	The expected value of X is 14.
	e.	Pr(X = 19)+ Pr(X = 1)= 1

Answer 1

We know Binomial Random Distribution is given as

Where, x = {0,1,2,3,4.......,n}

As per the question :-

n = 20

p = 0.7

Lets see each statement one by one :

a. Maximum possible value of x is 20 :- As we know x ranges from {0,1,2,3.....,n}. Here n = 20. Hence maximum value of x is 20. So it's correct

b. Minimum possible value of x is 0 :- As we know binomial random variable x ranges from {0,1,2,3,4.....,n}. So the minimum possible value of x is 0. So it's correct

c. Variance of X is 4.2 :- We know that the variance of a binomial random variable is given as

So using the values

So it's correct

d. Expected value of X is 4.2 :- We know expected value or mean of binomial distribution is given as

So it's correct

e. P(X=19) + P(X=1) = 1

We can put the values in the binomial function as given earlier

So,

So, It's wrong

Hence, Statement e. is wrong