Question

Suppose we have 4 students and we take their phones then return the phones to them randomly. Let X be the number of students who receive their own phone. Create a probability distribution chart for X.

Answer 1

We have 4 students & we take their phones then return the phones to them randomly.

Let, X be the number of students who receive their own phone

n - number of students = 4

p - Probability that student will receive their own phone = 1/4 = 0.25

X ~ Binomial (n = 4, p = 0.25)

PMF of binomial distribution -

; x = 0,1,2,......,n ; 0 p 1 ; p + q = 1

= 0 ; otherwise

X will take values 0,1,2,3,4.

= (1)(1)(0.3164) = 0.3164

= (4)(0.25)(0.4219) = 0.4219

= (6)(0.0625)(0.5625) = 0.2109

= (4)(0.0156)(0.75) = 0.0468

= (1)(0.0039)(1) = 0.0039

Probability distribution chart for X -

X	0	1	2	3	4	Total
P(X=x)	0.3164	0.4219	0.2109	0.0468	0.0039	1