Answer to Question #305852 in Statistics and Probability for Cris

Question

Problem:

Five coins are tossed. Let G be the random variable representing the number of heads (H) that occur. Find the values of the random variable G.

What to find:

1. The number of possible outcomes or sample space (S). 2. The sample spaces (place in the table).

3. The correct values of random variable G.

4. Interpretation or description about the value of the random variable G.

Answer 1

a)

Let G be the random variable representing the number of heads (H) that occur. Also, let T be the random variable representing the number of heads (T) that occur.

Suppose;

a) No head occurs in for the five tosses: , then, G=0

b)1 head and four tails occur, then, G=1

c)2 heads and 3 tails occur, then G = 2

d)3heads and 2tails occur, then G = 3

e)4heads and 1 tail occur, then, G=4

f)5 heads and no tail occurs, then, G=5

b)

G Sample spaces

0 {TTTTT}

1 {HTTTT, THTTT,TTHTT, TTTHT,TTTTH}

2 {HHTTT,HTHTT,HTTHT,HTTTH,THHTT,THTHT,THTTH,TTHHT, TTHTH,TTTHH}

3 {HHHTT,HHTHT,HHTTH,HTHTH, HTHHT,,HTTHH,THTHH, TTHHH,THHHT,THHTH}

4 {HHHHT, HHHTH,HHTHH,HTHHH,THHHH}

5 {HHHHH}

c.

The possible values for the random variable G = 0,1,2,3,4,5.

d.

The value of G represents the possible number of heads that can occur when each of the five distinct coins are tossed once, where order does not matter and replacements are not allowed.