1. A random experiment consists of throwing 4 equal coins, if X is the number of tails:a. Find the probability distribution of X and plot your graphb. What is the most likely tail number? Which one is the least likely?c. What is the average number of tails that come out, when throwing the four coins? d. What is the dispersion of X?

Question
Asked Nov 5, 2019

1. A random experiment consists of throwing 4 equal coins, if X is the number of tails:

a. Find the probability distribution of X and plot your graph

b. What is the most likely tail number? Which one is the least likely?

c. What is the average number of tails that come out, when throwing the four coins? d. What is the dispersion of X?

check_circleExpert Solution
Step 1

Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any specific question to be answered then please submit that question only or specify the question number in your message.”

(a)

The outcome for throwing 4 equal coins is,

HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT.

Thus, the total number of outcomes is 16.

The probability distribution of X is,

XNumber of outcomes with X tails
Probability
1/16 0.0625
0
4
4/16 0.25
1
6/16 0.375
2
6
4/16 0.25
4
1/16 0.0625
4
1
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Image Transcriptionclose

XNumber of outcomes with X tails Probability 1/16 0.0625 0 4 4/16 0.25 1 6/16 0.375 2 6 4/16 0.25 4 1/16 0.0625 4 1

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Step 2

Step by step procedure to plot the graph using MINITAB software is given below:

  • Choose Graph > Time Series Plot or Stat > Time Series > Time Series Plot.
  • Choose Simple, and then click OK.
  • In Series, enter P(X).
  • In Time and Scale, enter X under Stamp.
  • Click OK.

Output using the MINITAB software is given below:

Plot of PX)
0.40
0.35
0.30
025
020
a15
0.10
0,05
0
2
3
х
(x)d
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Image Transcriptionclose

Plot of PX) 0.40 0.35 0.30 025 020 a15 0.10 0,05 0 2 3 х (x)d

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Step 3

(b)

From the plot, it is observed that the most likely tail number is 2, because the probability value is greater for X=2 and the least likely is 0 and 4 because the probability value is lesser when compare...

E (x)=xP(x)
= 0(0.0625)+1(0.25) + 2(0.375) + 3(0.25)+ 4(0.0625)
0+0.250.75+0.75 +0.25
=2
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Image Transcriptionclose

E (x)=xP(x) = 0(0.0625)+1(0.25) + 2(0.375) + 3(0.25)+ 4(0.0625) 0+0.250.75+0.75 +0.25 =2

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