Answer to Question #297326 in Statistics and Probability for Kram

Question

Construct the probability distribution for each random variable X.

a. The random variable X represents the number of heads that occur when you toss 4 coins at the same time.

b. The random variable X represents the number of male children in a 3-child family.

c. The random variable X represents the amount gain by a person who buys s 20 peso ticket from a total of 1000 tickets for a raffle whose winner will obtain ₱5,000

Answer 1

a) Let S be the sample space

S= { HHHH, HHHT,HHTH,HHTT,HTHH,HTHT,HTTH,HTTT,THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT}

Let X be the number of heads that can occur. Then X can take values 0,1,2,3,4

p( x=0) =1/16

p( x=1) = 4/16 = 1/4

p( x= 2) = 6/16 = 3/8

p(x=3) = 4/16 = 1/4

p(x=4) = 1/16

The probability distribution can be expressed as below

x 0 1 2 3 4

p(x) 1/16 1/4 3/8 1/4 1/16

b) Let m represent the number of male and f female. Assuming that Males and females have an equal chance of occurrence we define the sample space as below

S = { mmm, mmf, mfm, mff,fff, ffm, fmf, fmm }

Let X be the number of males that can occur

p(x=0) = 1/8

p(x=1) = 3/8

p( x= 2) = 3/8

p(x=3) = 1/8

Thus the probability distribution can be expressed as below

x 0 1 2 3

p(x) 1/8 3/8 3/8 1/8

c) Define a random variable X representing the amount gained by a person who buys a 20 peso ticket from a total of 1000 tickets for a raffle whose winner will obtain P5000

Thus the probability distribution is defined as below

p(x) = ( 20/N ) where N is the total number of tickets

Hence p(x) = 20/1000 = 0.02 which is the required probability distribution.