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

Differential equation of newton’s law of cooling , 1. A direction ?eld for...

1. A direction ?eld for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step

Compositions of relations, Let Consider R A Χ B, S B Χ C be two relation...

Let Consider R A Χ B, S B Χ C be two relations. Then compositions of the relations S and R given by SoR A Χ C and is explained by (a, c) €(S o R) iff € b € B like (a, b) € R,

Calculus!, x+2y^2=63 and 4x+y^2=0; Find the area of the regions enclosed by...

x+2y^2=63 and 4x+y^2=0; Find the area of the regions enclosed by the lines and curves.

Sketch the graph f ( x ) = - x5 + (5/2 )x4 + (40/3) x3 + 5, Sketch the grap...

Sketch the graph of the below function. f ( x ) = - x 5 + (5/2 )x 4 + (40/3) x 3 + 5 Solution : Whenever we sketch a graph it's good to have a few points on the graph to

Find out the minimum distance from the origin, Problem 1. Find the maximum...

Problem 1. Find the maximum and the minimum distance from the origin to the ellipse x 2 + xy + y 2 = 3. Hints: (i) Use x 2 + y 2 as your objective function; (ii) You c

How do children learn maths?, HOW DO CHILDREN LEARN? : Have you ever tried...

HOW DO CHILDREN LEARN? : Have you ever tried teaching a young child what "ball" means? Did you do it by a lot of verbal description" Or did you let the child actually handle a b

World problem, Buses to Acton leave a bus station every 24 minutes. Buses t...

Buses to Acton leave a bus station every 24 minutes. Buses to Barton leave the same bus station every 20 minutes. A bus to Acton and a bus to Barton both leave the bus station at 9

Definition of logarithms, Q. Definition of Logarithms? Ans. A loga...

Q. Definition of Logarithms? Ans. A logarithm to the base a of a number x is the power to which a is raised to get x. In equation format: If x = a y , then log a  x

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