Question

Suppose in one of our quiz, there are 5 true-false questions. Assume you pick your answer by random guess. Let X be the number of your correct answers. Give out the distribution of X.

Answer 1

number of question=5 and Probability of correct answer=0.5( two choice, True and False)

here we use binomial distribution with parameter n=5 and p=0.5

let X is a random variable of correct answer

Binomial distribution ,P(X=r)=ⁿC_rp^r(1-p)^n-r  

the distribution of X is given as

X	P(X=x)
0	0.03125
1	0.15625
2	0.31250
3	0.31250
4	0.15625
5	0.03125

followign information has been generated using ms-excel

X	P(X=x)	using ms-excel command
0	0.03125	BINOMDIST(0,5,0.5,0)
1	0.15625	BINOMDIST(1,5,0.5,0)
2	0.31250	BINOMDIST(2,5,0.5,0)
3	0.31250	BINOMDIST(3,5,0.5,0)
4	0.15625	BINOMDIST(4,5,0.5,0)
5	0.03125	BINOMDIST(5,5,0.5,0)