The probability distribution of the random variable X is given by the formula P(X = x) = 0.09+0.01x^2 for x= 1,2,3,4,5 ). Find E(X).

The expected value of a discrete variable is defined as:

E(X) = ∑x*P(X=x) (for all possible values of x, in this case x = {1,2,3,4,5} ) 

(next, we will expand the summation and substitute in the values given, we are able to find P(X=x) simply by substituting in the equation from above)

= 1*(0.09+0.011^2) + 2(0.09+0.012^2) + 3(0.09+0.013^2) + 4(0.09+0.014^2) + 5(0.09+0.01*5^2)

(next, we will factorize in order to make calculation easier and less prone to mistakes)

= 0.09(1+2+3+4+5) + 0.01*(11^2 + 22^2 + 33^2 + 44^2 + 5*5^2)

(next, we will add up the first bracket and simplify the second bracket)

= 0.09*(15) + 0.01*(1^3 + 2^3 + 3^3 + 4^3 +5^3)

(next, we will multiply through the first bracket and multiply the individual expressions in the second bracket)

= 1.35 + 0.01*(1 + 8 + 27 + 64 + 125)

(next, we add up the second bracket)

= 1.35 + 0.01*(225)

= 1.35 + 2.25 = 3.6

E(X) = 3.6 (the expected value of X is 3.6)

RH
Answered by Robin H. Maths tutor

7223 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I show that (cos^4x - sin^4x) / cos^2x = 1 - tan^2x


The equation of a line is y=e(^2x)-9 and the line has points at (0,a) and (b,0). Find the values of a and b.


The equation of curve C is 3x^2 + xy + y^2 - 4x - 6y + 7 = 0. Use implicit differentiation to find dy/dx in terms of x and y.


A curve C has equation: x^3+2xy-x-y^3-20=0. Find dy/dx in terms of x and y.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences