Calculate the mean, variance & standard deviation, Mathematics

Assignment Help:

Calculate the mean, variance & standard deviation of the number of heads in a simultaneous toss of three coins. 

  SOLUTION: 

 Let X denotes the number of heads in a simultaneous toss of three coins. Then, X  can take values 0,1,2,3. 

NOW,        

             P(X=0)=P(TTT)=1/8 

            P(X=1)=P(HTT or TTH or THT)=3/8 

            P(X=2)=P(HHT or THH or HTH)=3/8 And,

            P(X=3)=P(HHH)=1/8 

Thus, the probability distribution of X is given by 

    X:  0     1      2     3  

P(X):1/8  3/8  3/8  1/8             

                     Computation of mean and variance

xi

0

1

2

3

 

pi

1/8

3/8

3/8

1/8

 

               

             Pi xi :  0          3/8          6/8        3/8          ∑pixi=3/2 

           Pi xi²:       0         3/8          12/8        9/8        ∑pixi=3 

 

WE HAVE,

              -

              X= MEAN = ∑ Pi xi  = 3/2 

         Var(X)= ∑ Pi xi ² – (∑pi xi)² = 3 – (3/2)² = ¾ 

      Standard deviation = √3/2 = 0.87


Related Discussions:- Calculate the mean, variance & standard deviation

find the vector projection - vectors, Given the vectors u = 3 i - 2 j ...

Given the vectors u = 3 i - 2 j + k ,   v = i + 2 j - 4 k ,    w = -2 i + 4 j - 5 k use vector methods to answer the following: (a) Prove u , v and w can form

Addition, in kannaha tiger reserve forest,there are 50 tigers and in bandha...

in kannaha tiger reserve forest,there are 50 tigers and in bandhavgarh reserve forest there are 35 tigers.how many tigers are there in all in both the forests

Discontinuous integrand- integration techniques, Discontinuous Integrand- I...

Discontinuous Integrand- Integration Techniques Here now we need to look at the second type of improper integrals that we will be looking at in this section.  These are integr

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

7th grade math, it cost $520 to plant 4 acres of corn. how much would it co...

it cost $520 to plant 4 acres of corn. how much would it cost to plant 3/5 acre of corn

Permuation and combination, how many words can be formed from letters of wo...

how many words can be formed from letters of word daughter such that each word contain 2vowles and 3consonant

..Job, Eddie mkes $15.75 per hour. Estimate how much Eddie will make per ye...

Eddie mkes $15.75 per hour. Estimate how much Eddie will make per year if he works 40 hours per week and 50 weeks per year.

How to adding polynomials, How to Adding Polynomials? The numerical par...

How to Adding Polynomials? The numerical part of a monomial is called the coefficient. For example, the coefficient of 5x is 5. The coefficient of -7a 2 b 3 is -7. Like

Determine the nand gate, Find out the two inputs when the NAND gate output ...

Find out the two inputs when the NAND gate output will be low. Ans. The output of NAND gate will be low if the two inputs are 11. The Truth Table of NAND gate is shown

Graphs of sin x and cos x, Q. Graphs of Sin x and Cos x ? Ans. The...

Q. Graphs of Sin x and Cos x ? Ans. The sine and cosine functions are related to the path that an object might take around a circle. Suppose a dolphin was swimming over

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd